diff --git a/test/porousmediumflow/1pnc/dispersion/CMakeLists.txt b/test/porousmediumflow/1pnc/dispersion/CMakeLists.txt
index 1295ced2619f69e120bcca2360a6b33077b47a5b..5da70223cc38fb481c041b7e29542959fde18611 100644
--- a/test/porousmediumflow/1pnc/dispersion/CMakeLists.txt
+++ b/test/porousmediumflow/1pnc/dispersion/CMakeLists.txt
@@ -36,3 +36,40 @@ dumux_add_test(NAME test_1pnc_dispersion_fulldispersiontensor_anisotropic
                         --command "${CMAKE_CURRENT_BINARY_DIR}/test_1pnc_dispersion_fulldispersiontensor_anisotropic params.input
                         -Problem.Name test_1pnc_dispersion_fulldispersiontensor_anisotropic
                         -Problem.DispersionTensor '1e-6 5e-8 6e-9 5e-6'")
+
+dumux_add_test(NAME test_1pncni_dispersion_scheidegger
+              LABELS porousmediumflow dispersion 1pncni
+              SOURCES main.cc
+              COMPILE_DEFINITIONS TYPETAG=OnePNCNIDispersionTestBox SCHEIDEGGER=1 NONISOTHERMAL=1
+              COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+              CMD_ARGS  --script fuzzy
+                        --files ${CMAKE_SOURCE_DIR}/test/references/test_1pncni_dispersion_scheidegger-reference.vtu
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_1pncni_dispersion_scheidegger-00026.vtu
+                        --command "${CMAKE_CURRENT_BINARY_DIR}/test_1pncni_dispersion_scheidegger params.input
+                        -Problem.Name test_1pncni_dispersion_scheidegger
+                        -Problem.AlphaL 0.1
+                        -Problem.AlphaT 0.01")
+
+dumux_add_test(NAME test_1pncni_dispersion_fulldispersiontensor_isotropic
+              LABELS porousmediumflow dispersion 1pncni
+              SOURCES main.cc
+              COMPILE_DEFINITIONS TYPETAG=OnePNCNIDispersionTestBox SCHEIDEGGER=0 NONISOTHERMAL=1
+              COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+              CMD_ARGS  --script fuzzy
+                        --files ${CMAKE_SOURCE_DIR}/test/references/test_1pncni_dispersion_fulldispersiontensor_isotropic-reference.vtu
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_1pncni_dispersion_fulldispersiontensor_isotropic-00026.vtu
+                        --command "${CMAKE_CURRENT_BINARY_DIR}/test_1pncni_dispersion_fulldispersiontensor_isotropic params.input
+                        -Problem.Name test_1pncni_dispersion_fulldispersiontensor_isotropic
+                        -Problem.DispersionTensor 1e-6")
+
+dumux_add_test(NAME test_1pncni_dispersion_fulldispersiontensor_anisotropic
+              LABELS porousmediumflow dispersion 1pncni
+              SOURCES main.cc
+              COMPILE_DEFINITIONS TYPETAG=OnePNCNIDispersionTestBox SCHEIDEGGER=0 NONISOTHERMAL=1
+              COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+              CMD_ARGS  --script fuzzy
+                        --files ${CMAKE_SOURCE_DIR}/test/references/test_1pncni_dispersion_fulldispersiontensor_anisotropic-reference.vtu
+                                ${CMAKE_CURRENT_BINARY_DIR}/test_1pncni_dispersion_fulldispersiontensor_anisotropic-00026.vtu
+                        --command "${CMAKE_CURRENT_BINARY_DIR}/test_1pncni_dispersion_fulldispersiontensor_anisotropic params.input
+                        -Problem.Name test_1pncni_dispersion_fulldispersiontensor_anisotropic
+                        -Problem.DispersionTensor '1e-6 5e-8 6e-9 5e-6'")
diff --git a/test/porousmediumflow/1pnc/dispersion/main.cc b/test/porousmediumflow/1pnc/dispersion/main.cc
index 458d7417cc54491c50a45f8da44a40ca748f3856..ba323a42c18ece9148afd86d93798b331f64aa1a 100644
--- a/test/porousmediumflow/1pnc/dispersion/main.cc
+++ b/test/porousmediumflow/1pnc/dispersion/main.cc
@@ -24,15 +24,11 @@
 
 #include <config.h>
 
-#include <ctime>
 #include <iostream>
 
 #include <dune/common/parallel/mpihelper.hh>
 #include <dune/common/timer.hh>
-#include <dune/grid/io/file/vtk.hh>
-#include <dune/istl/io.hh>
 
-#include <dumux/discretization/method.hh>
 
 #include <dumux/common/properties.hh>
 #include <dumux/common/parameters.hh>
@@ -44,7 +40,8 @@
 #include <dumux/assembly/fvassembler.hh>
 
 #include <dumux/io/vtkoutputmodule.hh>
-#include <dumux/io/grid/gridmanager.hh>
+#include <dumux/io/grid/gridmanager_yasp.hh>
+#include <dumux/io/grid/gridmanager_ug.hh>
 
 #include "properties.hh"
 
diff --git a/test/porousmediumflow/1pnc/dispersion/params.input b/test/porousmediumflow/1pnc/dispersion/params.input
index 6757d750114c14f4cb0ab3415e1cb0c9e5160e91..3bb32efd41d9a7afe200b7b51282233a6e6a825c 100644
--- a/test/porousmediumflow/1pnc/dispersion/params.input
+++ b/test/porousmediumflow/1pnc/dispersion/params.input
@@ -11,6 +11,7 @@ Cells = 20 20
 Name = default
 EnableGravity = true
 BoundaryConcentration = 0.04 # molfrac
+BoundaryTemperatureDifference = 3 # K
 CounterFlowRate = 1e-4
 Pressure = 1e5
 AlphaL = 0.1 # longitual dispersivity
@@ -22,3 +23,8 @@ UseLineSearch = true
 
 [Vtk]
 AddVelocity = 1 # enable velocity output
+
+[Component]
+SolidDensity = 2700
+SolidThermalConductivity = 2.8
+SolidHeatCapacity = 790
diff --git a/test/porousmediumflow/1pnc/dispersion/problem.hh b/test/porousmediumflow/1pnc/dispersion/problem.hh
index b0978d6665f3ea415cc5ea7bee745091dcb6c174..5de2f0b761d79f12e4d11248fbff50d01bad8508 100644
--- a/test/porousmediumflow/1pnc/dispersion/problem.hh
+++ b/test/porousmediumflow/1pnc/dispersion/problem.hh
@@ -87,13 +87,15 @@ class OnePNCDispersionProblem : public PorousMediumFlowProblem<TypeTag>
 
     enum
     {
+#if NONISOTHERMAL
+        energyEqIdx = Indices::energyEqIdx,
+#endif
         // indices of the primary variables
         pressureIdx = Indices::pressureIdx,
 
         // component indices
         H2OIdx = FluidSystem::compIdx(FluidSystem::MultiPhaseFluidSystem::H2OIdx),
         N2Idx = FluidSystem::compIdx(FluidSystem::MultiPhaseFluidSystem::N2Idx),
-
         // indices of the equations
         contiH2OEqIdx = Indices::conti0EqIdx + H2OIdx,
         contiN2EqIdx = Indices::conti0EqIdx + N2Idx
@@ -119,6 +121,7 @@ public:
             std::cout<<"problem uses mass fractions" << '\n';
 
         boundaryConcentration_ = getParam<Scalar>("Problem.BoundaryConcentration");
+        temperatureDifference_ = getParam<Scalar>("Problem.BoundaryTemperatureDifference");
         counterFlowRate_ = getParam<Scalar>("Problem.CounterFlowRate");
         pressure_ = getParam<Scalar>("Problem.Pressure");
         problemName_ = getParam<std::string>("Problem.Name");
@@ -169,6 +172,9 @@ public:
         if (isLeftBoundary_(globalPos))
         {
             values[contiN2EqIdx] =  boundaryConcentration_;
+#if NONISOTHERMAL
+            values[energyEqIdx] = temperature() + temperatureDifference_;
+#endif
         }
 
         return values;
@@ -201,7 +207,7 @@ public:
         const auto globalPos = element.geometry().corner(scvf.insideScvIdx());
         NumEqVector values(0.0);
         if (isRightBoundary_(globalPos))
-            values[contiH2OEqIdx] = -1.0 * counterFlowRate_; //-5E-2; //5e-5*m2/s*1000kg/m^3
+            values[contiH2OEqIdx] = -1.0 * counterFlowRate_;
         return values;
     }
 
@@ -233,6 +239,9 @@ public:
 
         values[Indices::pressureIdx] = pressure_ - (density * gravity * depth); //initial condition for the pressure
         values[contiN2EqIdx] = 0.0; //initial condition for the molefraction
+#if NONISOTHERMAL
+        values[energyEqIdx] = temperature();
+#endif
         return values;
     }
 
@@ -252,6 +261,7 @@ private:
     static constexpr Scalar eps_ = 1e-6;
     Scalar pressure_;
     Scalar counterFlowRate_;
+    Scalar temperatureDifference_;
     Scalar boundaryConcentration_;
     std::string problemName_;
 };
diff --git a/test/porousmediumflow/1pnc/dispersion/properties.hh b/test/porousmediumflow/1pnc/dispersion/properties.hh
index f016eec52b74d24099e825bc02766a878633fe4b..160a623eeb488fde71c8180fbb5d8cf81fd07ef9 100644
--- a/test/porousmediumflow/1pnc/dispersion/properties.hh
+++ b/test/porousmediumflow/1pnc/dispersion/properties.hh
@@ -31,6 +31,10 @@
 #endif
 #include <dune/grid/yaspgrid.hh>
 
+#ifndef NONISOTHERMAL // default to false if not set through CMake
+#define NONISOTHERMAL false
+#endif
+
 #include <dumux/common/math.hh>
 
 #include <dumux/discretization/cctpfa.hh>
@@ -54,6 +58,7 @@ namespace Dumux::Properties {
 namespace TTag {
 struct DispersionTest { using InheritsFrom = std::tuple<BoxModel>; };
 struct OnePNCDispersionTestBox { using InheritsFrom = std::tuple<DispersionTest, OnePNC>; };
+struct OnePNCNIDispersionTestBox { using InheritsFrom = std::tuple<DispersionTest, OnePNCNI>; };
 } // end namespace TTag
 
 // Set the grid type
@@ -95,6 +100,7 @@ template<class TypeTag>
 struct EnableCompositionalDispersion<TypeTag, TTag::DispersionTest> { static constexpr bool value = true; };
 
 template<class TypeTag>
+struct EnableThermalDispersion<TypeTag, TTag::DispersionTest> { static constexpr bool value = NONISOTHERMAL; };
 
 template<class TypeTag>
 struct DispersionFluxType<TypeTag, TTag::DispersionTest> { using type = OnePDiffusiveDispersionFlux<TypeTag>; };
diff --git a/test/references/test_1pncni_dispersion_fulldispersiontensor_anisotropic-reference.vtu b/test/references/test_1pncni_dispersion_fulldispersiontensor_anisotropic-reference.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..bdc2daafab5c1d81db8ee93de125daf54244c6ff
--- /dev/null
+++ b/test/references/test_1pncni_dispersion_fulldispersiontensor_anisotropic-reference.vtu
@@ -0,0 +1,836 @@
+<?xml version="1.0"?>
+<VTKFile type="UnstructuredGrid" version="0.1" byte_order="LittleEndian">
+  <UnstructuredGrid>
+    <Piece NumberOfCells="400" NumberOfPoints="441">
+      <PointData Scalars="p" Vectors="velocity_liq (m/s)">
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diff --git a/test/references/test_1pncni_dispersion_fulldispersiontensor_isotropic-reference.vtu b/test/references/test_1pncni_dispersion_fulldispersiontensor_isotropic-reference.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..d8a301132b5356362bb4d0d39338cc376b3a0ab0
--- /dev/null
+++ b/test/references/test_1pncni_dispersion_fulldispersiontensor_isotropic-reference.vtu
@@ -0,0 +1,836 @@
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diff --git a/test/references/test_1pncni_dispersion_scheidegger-reference.vtu b/test/references/test_1pncni_dispersion_scheidegger-reference.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..fa0961c99999a1187dcceb15840e456c65cbb5db
--- /dev/null
+++ b/test/references/test_1pncni_dispersion_scheidegger-reference.vtu
@@ -0,0 +1,836 @@
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