diff --git a/test/multidomain/facet/1pnc_1pnc/CMakeLists.txt b/test/multidomain/facet/1pnc_1pnc/CMakeLists.txt
index 8f009f87d5db2272800ed8a6bb868305b92693a7..58d318bb25e11581989f23f65508627638ececc0 100644
--- a/test/multidomain/facet/1pnc_1pnc/CMakeLists.txt
+++ b/test/multidomain/facet/1pnc_1pnc/CMakeLists.txt
@@ -48,6 +48,58 @@ dumux_add_test(NAME test_md_facet_1pnc1pnc_box
                          --zeroThreshold {"delp":1e-3}
                          --command "${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1pnc1pnc_box params.input -Vtk.OutputName test_md_facet_1pnc1pnc_box")
 
+dumux_add_test(NAME test_md_facet_1pncni1pncni_tpfa
+               SOURCES main.cc
+               LABELS multidomain multidomain_facet 1pnc
+               COMPILE_DEFINITIONS BULKTYPETAG=OnePNCNIBulkTpfa
+               COMPILE_DEFINITIONS FACETTYPETAG=OnePNCNIFacetTpfa
+               COMPILE_DEFINITIONS DIMWORLD=2
+               COMPILE_DEFINITIONS BULKGRID=Dune::ALUGrid<2,2,Dune::cube,Dune::nonconforming>
+               CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-alugrid_FOUND )"
+               COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+               CMD_ARGS  --script fuzzy
+                         --files ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_1pncni1pncni_tpfa_bulk-reference.vtu
+                                 ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1pncni1pncni_tpfa_bulk-00019.vtu
+                                 ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_1pncni1pncni_tpfa_facet-reference.vtp
+                                 ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1pncni1pncni_tpfa_facet-00019.vtp
+                         --zeroThreshold {"delp":1e-3}
+                         --command "${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1pncni1pncni_tpfa params.input -Vtk.OutputName test_md_facet_1pncni1pncni_tpfa")
+
+dumux_add_test(NAME test_md_facet_1pncni1pncni_mpfa
+               SOURCES main.cc
+               LABELS multidomain multidomain_facet 1pnc
+               COMPILE_DEFINITIONS BULKTYPETAG=OnePNCNIBulkMpfa
+               COMPILE_DEFINITIONS FACETTYPETAG=OnePNCNIFacetTpfa
+               COMPILE_DEFINITIONS DIMWORLD=2
+               COMPILE_DEFINITIONS BULKGRID=Dune::ALUGrid<2,2,Dune::cube,Dune::nonconforming>
+               CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-alugrid_FOUND )"
+               COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+               CMD_ARGS  --script fuzzy
+                         --files ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_1pncni1pncni_tpfa_bulk-reference.vtu
+                                 ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1pncni1pncni_mpfa_bulk-00019.vtu
+                                 ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_1pncni1pncni_tpfa_facet-reference.vtp
+                                 ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1pncni1pncni_mpfa_facet-00019.vtp
+                         --zeroThreshold {"delp":1e-3}
+                         --command "${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1pncni1pncni_mpfa params.input -Vtk.OutputName test_md_facet_1pncni1pncni_mpfa")
+
+dumux_add_test(NAME test_md_facet_1pncni1pncni_box
+               SOURCES main.cc
+               LABELS multidomain multidomain_facet 1pnc
+               COMPILE_DEFINITIONS BULKTYPETAG=OnePNCNIBulkBox
+               COMPILE_DEFINITIONS FACETTYPETAG=OnePNCNIFacetBox
+               COMPILE_DEFINITIONS DIMWORLD=2
+               COMPILE_DEFINITIONS BULKGRID=Dune::ALUGrid<2,2,Dune::cube,Dune::nonconforming>
+               CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-alugrid_FOUND )"
+               COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+               CMD_ARGS  --script fuzzy
+                         --files ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_1pncni1pncni_box_bulk-reference.vtu
+                                 ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1pncni1pncni_box_bulk-00019.vtu
+                                 ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_1pncni1pncni_box_facet-reference.vtp
+                                 ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1pncni1pncni_box_facet-00019.vtp
+                         --zeroThreshold {"delp":1e-3}
+                         --command "${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1pncni1pncni_box params.input -Vtk.OutputName test_md_facet_1pncni1pncni_box")
+
+
 dumux_add_test(NAME test_md_facet_1pnc1pnc_surface_tpfa
                SOURCES main.cc
                LABELS multidomain multidomain_facet 1pnc
@@ -96,3 +148,52 @@ dumux_add_test(NAME test_md_facet_1pnc1pnc_surface_box
                                  ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1pnc1pnc_surface_box_facet-00018.vtp
                          --zeroThreshold {"delp":1e-3}
                          --command "${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1pnc1pnc_surface_box params.input -Vtk.OutputName test_md_facet_1pnc1pnc_surface_box -Grid.File grids/square_surface.msh")
+
+dumux_add_test(NAME test_md_facet_1pncni1pncni_surface_tpfa
+               SOURCES main.cc
+               LABELS multidomain multidomain_facet 1pnc
+               COMPILE_DEFINITIONS BULKTYPETAG=OnePNCNIBulkTpfa
+               COMPILE_DEFINITIONS FACETTYPETAG=OnePNCNIFacetTpfa
+               COMPILE_DEFINITIONS DIMWORLD=3
+               CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-alugrid_FOUND )"
+               COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+               CMD_ARGS  --script fuzzy
+                         --files ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_1pncni1pncni_surface_tpfa_bulk-reference.vtu
+                                 ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1pncni1pncni_surface_tpfa_bulk-00019.vtu
+                                 ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_1pncni1pncni_surface_tpfa_facet-reference.vtp
+                                 ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1pncni1pncni_surface_tpfa_facet-00019.vtp
+                         --zeroThreshold {"delp":1e-3}
+                         --command "${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1pncni1pncni_surface_tpfa params.input -Vtk.OutputName test_md_facet_1pncni1pncni_surface_tpfa -Grid.File grids/square_surface.msh")
+
+dumux_add_test(NAME test_md_facet_1pncni1pncni_surface_mpfa
+               SOURCES main.cc
+               LABELS multidomain multidomain_facet 1pnc
+               COMPILE_DEFINITIONS BULKTYPETAG=OnePNCNIBulkMpfa
+               COMPILE_DEFINITIONS FACETTYPETAG=OnePNCNIFacetTpfa
+               COMPILE_DEFINITIONS DIMWORLD=3
+               CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-alugrid_FOUND )"
+               COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+               CMD_ARGS  --script fuzzy
+                         --zeroThreshold {"delp":1e-8}
+                         --files ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_1pncni1pncni_surface_tpfa_bulk-reference.vtu
+                                 ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1pncni1pncni_surface_mpfa_bulk-00020.vtu
+                                 ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_1pncni1pncni_surface_tpfa_facet-reference.vtp
+                                 ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1pncni1pncni_surface_mpfa_facet-00020.vtp
+                         --zeroThreshold {"delp":1e-3}
+                         --command "${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1pncni1pncni_surface_mpfa params.input -Vtk.OutputName test_md_facet_1pncni1pncni_surface_mpfa -Grid.File grids/square_surface.msh")
+
+dumux_add_test(NAME test_md_facet_1pncni1pncni_surface_box
+               SOURCES main.cc
+               LABELS multidomain multidomain_facet 1pnc
+               COMPILE_DEFINITIONS BULKTYPETAG=OnePNCNIBulkBox
+               COMPILE_DEFINITIONS FACETTYPETAG=OnePNCNIFacetBox
+               COMPILE_DEFINITIONS DIMWORLD=3
+               CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-alugrid_FOUND )"
+               COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+               CMD_ARGS  --script fuzzy
+                         --files ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_1pncni1pncni_surface_box_bulk-reference.vtu
+                                 ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1pncni1pncni_surface_box_bulk-00019.vtu
+                                 ${CMAKE_SOURCE_DIR}/test/references/test_md_facet_1pncni1pncni_surface_box_facet-reference.vtp
+                                 ${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1pncni1pncni_surface_box_facet-00019.vtp
+                         --zeroThreshold {"delp":1e-3}
+                         --command "${CMAKE_CURRENT_BINARY_DIR}/test_md_facet_1pncni1pncni_surface_box params.input -Vtk.OutputName test_md_facet_1pncni1pncni_surface_box -Grid.File grids/square_surface.msh")
diff --git a/test/multidomain/facet/1pnc_1pnc/params.input b/test/multidomain/facet/1pnc_1pnc/params.input
index e2bbd60f630d2a774e63d4692b0de1f0d8ee5eec..04f2509103cf17a57f13512a4d64f391185aa975 100644
--- a/test/multidomain/facet/1pnc_1pnc/params.input
+++ b/test/multidomain/facet/1pnc_1pnc/params.input
@@ -22,5 +22,10 @@ SpatialParams.Porosity = 0.1
 [FacetCoupling]
 Xi = 1.0
 
+[Component]
+SolidDensity = 2700
+SolidThermalConductivity = 2.8
+SolidHeatCapacity = 790
+
 [Vtk]
 OutputName = test_md_facet_1pnc1pnc
diff --git a/test/multidomain/facet/1pnc_1pnc/problem_bulk.hh b/test/multidomain/facet/1pnc_1pnc/problem_bulk.hh
index 9640178b51f53e2edf47c73eb09f440962339549..c1bb5877256cd8efa24ff34af062f8f933fe41ba 100644
--- a/test/multidomain/facet/1pnc_1pnc/problem_bulk.hh
+++ b/test/multidomain/facet/1pnc_1pnc/problem_bulk.hh
@@ -47,21 +47,29 @@ namespace Properties {
 
 // create the type tag nodes
 namespace TTag {
-struct OnePNCBulk { using InheritsFrom = std::tuple<OnePNC>; };
+struct BaseBulk {};
+struct OnePNCBulk { using InheritsFrom = std::tuple<OnePNC, BaseBulk>; };
+struct OnePNCNIBulk { using InheritsFrom = std::tuple<OnePNCNI, BaseBulk>; };
+
 struct OnePNCBulkTpfa { using InheritsFrom = std::tuple<CCTpfaFacetCouplingModel, OnePNCBulk>; };
+struct OnePNCNIBulkTpfa { using InheritsFrom = std::tuple<CCTpfaFacetCouplingModel, OnePNCNIBulk>; };
+
 struct OnePNCBulkMpfa { using InheritsFrom = std::tuple<CCMpfaFacetCouplingModel, OnePNCBulk>; };
+struct OnePNCNIBulkMpfa { using InheritsFrom = std::tuple<CCMpfaFacetCouplingModel, OnePNCNIBulk>; };
+
 struct OnePNCBulkBox { using InheritsFrom = std::tuple<BoxFacetCouplingModel, OnePNCBulk>; };
+struct OnePNCNIBulkBox { using InheritsFrom = std::tuple<BoxFacetCouplingModel, OnePNCNIBulk>; };
 } // end namespace TTag
 
 // Set the grid type (DIMWORLD is defined in CMakeLists.txt)
 template<class TypeTag>
-struct Grid<TypeTag, TTag::OnePNCBulk> { using type = Dune::ALUGrid<2, DIMWORLD, Dune::cube, Dune::nonconforming>; };
+struct Grid<TypeTag, TTag::BaseBulk> { using type = Dune::ALUGrid<2, DIMWORLD, Dune::cube, Dune::nonconforming>; };
 // Set the problem type
 template<class TypeTag>
-struct Problem<TypeTag, TTag::OnePNCBulk> { using type = OnePNCBulkProblem<TypeTag>; };
+struct Problem<TypeTag, TTag::BaseBulk> { using type = OnePNCBulkProblem<TypeTag>; };
 // set the spatial params
 template<class TypeTag>
-struct SpatialParams<TypeTag, TTag::OnePNCBulk>
+struct SpatialParams<TypeTag, TTag::BaseBulk>
 {
     using type = OnePSpatialParams< GetPropType<TypeTag, Properties::GridGeometry>,
                                     GetPropType<TypeTag, Properties::Scalar> >;
@@ -69,7 +77,7 @@ struct SpatialParams<TypeTag, TTag::OnePNCBulk>
 
 // Set fluid configuration
 template<class TypeTag>
-struct FluidSystem<TypeTag, TTag::OnePNCBulk>
+struct FluidSystem<TypeTag, TTag::BaseBulk>
 {
 private:
     using Scalar = GetPropType<TypeTag, Properties::Scalar>;
@@ -108,6 +116,9 @@ class OnePNCBulkProblem : public PorousMediumFlowProblem<TypeTag>
     using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;
     using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>;
 
+    using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>;
+    static constexpr bool enableHeatConduction = ModelTraits::enableEnergyBalance();
+
     enum
     {
         // indices of the primary variables
@@ -164,8 +175,16 @@ public:
     PrimaryVariables dirichletAtPos(const GlobalPosition& globalPos) const
     {
         auto values = initialAtPos(globalPos);
+
         if (globalPos[1] < 1e-6)
+        {
             values[N2Idx] = 1e-3;
+            if constexpr (enableHeatConduction)
+            {
+                values[Indices::temperatureIdx] += 100; // DeltaT = 100 K
+            }
+        }
+
         return values;
     }
 
@@ -175,6 +194,12 @@ public:
         PrimaryVariables values;
         values[pressureIdx] = 1.0e5;
         values[N2Idx] = 0.0;
+
+        if constexpr (enableHeatConduction)
+        {
+            values[Indices::temperatureIdx] = temperature();
+        }
+
         return values;
     }
 
diff --git a/test/multidomain/facet/1pnc_1pnc/problem_facet.hh b/test/multidomain/facet/1pnc_1pnc/problem_facet.hh
index cd1123acaf308f6396c41e6d012fa00b5ae9e3d5..aae78ccace3be50998b959f3b7f33b603b127f83 100644
--- a/test/multidomain/facet/1pnc_1pnc/problem_facet.hh
+++ b/test/multidomain/facet/1pnc_1pnc/problem_facet.hh
@@ -45,20 +45,26 @@ namespace Properties {
 
 // create the type tag nodes
 namespace TTag {
-struct OnePNCFacet { using InheritsFrom = std::tuple<OnePNC>; };
+struct BaseFacet {};
+struct OnePNCFacet { using InheritsFrom = std::tuple<OnePNC, BaseFacet>; }; // Isothermal case
+struct OnePNCNIFacet { using InheritsFrom = std::tuple<OnePNCNI, BaseFacet>; }; // Non-Isothermal case
+
 struct OnePNCFacetTpfa { using InheritsFrom = std::tuple<OnePNCFacet, CCTpfaModel>; };
+struct OnePNCNIFacetTpfa { using InheritsFrom = std::tuple<OnePNCNIFacet, CCTpfaModel>; };
+
 struct OnePNCFacetBox { using InheritsFrom = std::tuple<OnePNCFacet, BoxModel>; };
+struct OnePNCNIFacetBox { using InheritsFrom = std::tuple<OnePNCNIFacet, BoxModel>; };
 } // end namespace TTag
 
 // Set the grid type
 template<class TypeTag>
-struct Grid<TypeTag, TTag::OnePNCFacet> { using type = Dune::FoamGrid<1, DIMWORLD>; };
+struct Grid<TypeTag, TTag::BaseFacet> { using type = Dune::FoamGrid<1, DIMWORLD>; };
 // Set the problem type
 template<class TypeTag>
-struct Problem<TypeTag, TTag::OnePNCFacet> { using type = OnePNCLowDimProblem<TypeTag>; };
+struct Problem<TypeTag, TTag::BaseFacet> { using type = OnePNCLowDimProblem<TypeTag>; };
 // set the spatial params
 template<class TypeTag>
-struct SpatialParams<TypeTag, TTag::OnePNCFacet>
+struct SpatialParams<TypeTag, TTag::BaseFacet>
 {
     using type = OnePSpatialParams< GetPropType<TypeTag, Properties::GridGeometry>,
                                     GetPropType<TypeTag, Properties::Scalar> >;
@@ -66,7 +72,7 @@ struct SpatialParams<TypeTag, TTag::OnePNCFacet>
 
 // the fluid system
 template<class TypeTag>
-struct FluidSystem<TypeTag, TTag::OnePNCFacet>
+struct FluidSystem<TypeTag, TTag::BaseFacet>
 {
 private:
     using Scalar = GetPropType<TypeTag, Properties::Scalar>;
@@ -105,6 +111,9 @@ class OnePNCLowDimProblem : public PorousMediumFlowProblem<TypeTag>
     using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;
     using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>;
 
+    using ModelTraits = GetPropType<TypeTag, Properties::ModelTraits>;
+    static constexpr bool enableHeatConduction = ModelTraits::enableEnergyBalance();
+
     enum
     {
         // indices of the primary variables
@@ -163,6 +172,12 @@ public:
         PrimaryVariables values;
         values[pressureIdx] = 1.0e5;
         values[N2Idx] = 0.0;
+
+        if constexpr (enableHeatConduction)
+        {
+            values[Indices::temperatureIdx] = temperature();
+        }
+
         return values;
     }
 
diff --git a/test/references/test_md_facet_1pncni1pncni_box_bulk-reference.vtu b/test/references/test_md_facet_1pncni1pncni_box_bulk-reference.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..b1633f80a9b96241ce99f46c0c0499750d35b98e
--- /dev/null
+++ b/test/references/test_md_facet_1pncni1pncni_box_bulk-reference.vtu
@@ -0,0 +1,1259 @@
+<?xml version="1.0"?>
+<VTKFile type="UnstructuredGrid" version="0.1" byte_order="LittleEndian">
+  <UnstructuredGrid>
+    <Piece NumberOfCells="728" NumberOfPoints="783">
+      <PointData Scalars="p">
+        <DataArray type="Float32" Name="p" NumberOfComponents="1" format="ascii">
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+          100000 100000 100000 100000 100000 100000 100000 100000 100000 100000 100000 100000
+          100000 100000 100000 100000 100000 100000 100000 100000 100000 100000 100000 100000
+          100000 100000 100000 100000 100000 100000 100000 100000 100000 100000 100000 100000
+          100000 100000 100000
+        </DataArray>
+        <DataArray type="Float32" Name="rho" NumberOfComponents="1" format="ascii">
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diff --git a/test/references/test_md_facet_1pncni1pncni_box_facet-reference.vtp b/test/references/test_md_facet_1pncni1pncni_box_facet-reference.vtp
new file mode 100644
index 0000000000000000000000000000000000000000..a56c4f01cd65738ff1183db076b69b0c03baa57c
--- /dev/null
+++ b/test/references/test_md_facet_1pncni1pncni_box_facet-reference.vtp
@@ -0,0 +1,70 @@
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diff --git a/test/references/test_md_facet_1pncni1pncni_surface_box_bulk-reference.vtu b/test/references/test_md_facet_1pncni1pncni_surface_box_bulk-reference.vtu
new file mode 100644
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diff --git a/test/references/test_md_facet_1pncni1pncni_surface_box_facet-reference.vtp b/test/references/test_md_facet_1pncni1pncni_surface_box_facet-reference.vtp
new file mode 100644
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diff --git a/test/references/test_md_facet_1pncni1pncni_surface_tpfa_bulk-reference.vtu b/test/references/test_md_facet_1pncni1pncni_surface_tpfa_bulk-reference.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..56e686eb2f35f900451dcab0a8e380325a7c22ab
--- /dev/null
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diff --git a/test/references/test_md_facet_1pncni1pncni_tpfa_facet-reference.vtp b/test/references/test_md_facet_1pncni1pncni_tpfa_facet-reference.vtp
new file mode 100644
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