diff --git a/modules/navier_stokes/test/tests/finite_volume/wcns/materials/1d_test_cpT.i b/modules/navier_stokes/test/tests/finite_volume/wcns/materials/1d_test_cpT.i
new file mode 100644
index 000000000000..9f2259c8540a
--- /dev/null
+++ b/modules/navier_stokes/test/tests/finite_volume/wcns/materials/1d_test_cpT.i
@@ -0,0 +1,231 @@
+L = 30
+bulk_u = 0.01
+p_ref = 101325.0
+T_in = 860
+q_source = 50000
+
+A_cp = 976.78
+B_cp = 1.0634
+rho = 2000
+
+advected_interp_method = 'upwind'
+
+[Mesh]
+  [gmg]
+    type = GeneratedMeshGenerator
+    dim = 1
+    xmin = 0
+    xmax = ${L}
+    nx = 10
+  []
+[]
+
+[GlobalParams]
+  rhie_chow_user_object = 'rc'
+  advected_interp_method = ${advected_interp_method}
+  velocity_interp_method = 'rc'
+[]
+
+[UserObjects]
+  [rc]
+    type = INSFVRhieChowInterpolator
+    u = vel_x
+    pressure = pressure
+  []
+[]
+
+[Variables]
+  [vel_x]
+    type = INSFVVelocityVariable
+    initial_condition = ${bulk_u}
+    two_term_boundary_expansion = false
+  []
+  [pressure]
+    type = INSFVPressureVariable
+    initial_condition = ${p_ref}
+    two_term_boundary_expansion = false
+  []
+  [T]
+    type = INSFVEnergyVariable
+    two_term_boundary_expansion = false
+    initial_condition = ${T_in}
+  []
+[]
+
+[FVKernels]
+  [mass]
+    type = WCNSFVMassAdvection
+    variable = pressure
+    rho = 'rho'
+  []
+
+  [u_advection]
+    type = INSFVMomentumAdvection
+    variable = vel_x
+    rho = 'rho'
+    momentum_component = 'x'
+  []
+  [u_viscosity]
+    type = INSFVMomentumDiffusion
+    variable = vel_x
+    mu = 'mu'
+    momentum_component = 'x'
+  []
+  [u_pressure]
+    type = INSFVMomentumPressure
+    variable = vel_x
+    momentum_component = 'x'
+    pressure = pressure
+  []
+
+  [temp_conduction]
+    type = FVDiffusion
+    coeff = 'k'
+    variable = T
+  []
+  [temp_advection]
+    type = INSFVEnergyAdvection
+    variable = T
+  []
+  [source]
+    type = FVBodyForce
+    variable = T
+    function = source_func
+  []
+[]
+
+[FVBCs]
+  [inlet-u]
+    type = INSFVInletVelocityBC
+    boundary = 'left'
+    variable = vel_x
+    functor = ${bulk_u}
+  []
+  [inlet_T]
+    type = FVDirichletBC
+    variable = T
+    boundary = 'left'
+    value = ${T_in}
+  []
+
+  [outlet_p]
+    type = INSFVOutletPressureBC
+    boundary = 'right'
+    variable = pressure
+    function = ${p_ref}
+  []
+[]
+
+[Functions]
+  [source_func]
+    type = ParsedFunction
+    expression = '${q_source}'
+  []
+[]
+
+[FunctorMaterials]
+  [converter_to_regular_T]
+    type = FunctorADConverter
+    ad_props_in = 'T'
+    reg_props_out = 'T_nAD'
+  []
+  [ins_fv]
+    type = INSFVEnthalpyFunctorMaterial
+    temperature = 'T'
+    rho = 'rho'
+    cp = 'cp'
+
+    assume_constant_cp = false
+    h_in = 'h'
+    # fp = 'fp'
+    # pressure = 'pressure'
+  []
+
+  [rho]
+    type = ADParsedFunctorMaterial
+    property_name = 'rho'
+    expression = '${rho}'
+  []
+  [mu]
+    type = ADParsedFunctorMaterial
+    property_name = 'mu'
+    expression = '4.5e-3'
+  []
+  [k]
+    type = ADParsedFunctorMaterial
+    property_name = 'k'
+    expression = '0.7'
+  []
+  [h]
+    type = ADParsedFunctorMaterial
+    property_name = 'h'
+    functor_names = 'T ${A_cp} ${B_cp}'
+    functor_symbols = 'T A_cp B_cp'
+    expression = 'A_cp * T + B_cp * T * T / 2'
+  []
+  [cp]
+    type = ADParsedFunctorMaterial
+    property_name = 'cp'
+    functor_names = 'T ${A_cp} ${B_cp}'
+    functor_symbols = 'T A_cp B_cp'
+    expression = 'A_cp+B_cp*T'
+  []
+[]
+
+[Executioner]
+  type = Steady
+  solve_type = 'NEWTON'
+  petsc_options_iname = '-pc_type -pc_factor_shift_type'
+  petsc_options_value = 'lu       NONZERO'
+
+  nl_abs_tol = 1e-9
+  nl_max_its = 50
+  line_search = 'none'
+
+  automatic_scaling = true
+  off_diagonals_in_auto_scaling = true
+[]
+
+[Postprocessors]
+  [H_in]
+    type = VolumetricFlowRate
+    vel_x = 'vel_x'
+    advected_quantity = 'rho_h'
+    boundary = 'left'
+  []
+  [H_out]
+    type = VolumetricFlowRate
+    vel_x = 'vel_x'
+    advected_quantity = 'rho_h'
+    boundary = 'right'
+  []
+  [Q]
+    type = FunctionElementIntegral
+    function = 'source_func'
+    execute_on = 'initial'
+  []
+  [balance_in_percent]
+    type = ParsedPostprocessor
+    expression = '(H_out + H_in - Q) / H_in * 100'
+    pp_names = 'H_in H_out Q'
+  []
+
+  [T_out]
+    type = SideAverageValue
+    variable = T
+    boundary = 'right'
+  []
+  [T_analytical]
+    type = Receiver
+    default = ${fparse (-A_cp+sqrt(A_cp^2-2*B_cp*(-q_source/rho/bulk_u*L-A_cp*T_in-B_cp/2*T_in*T_in)))/B_cp}
+  []
+  [error_T]
+    type = ParsedPostprocessor
+    expression = 'T_out - T_analytical'
+    pp_names = 'T_out T_analytical'
+  []
+[]
+
+[Outputs]
+  csv = true
+[]
diff --git a/modules/navier_stokes/test/tests/finite_volume/wcns/materials/gold/1d_test_cpT_out.csv b/modules/navier_stokes/test/tests/finite_volume/wcns/materials/gold/1d_test_cpT_out.csv
new file mode 100644
index 000000000000..3e302e7a961d
--- /dev/null
+++ b/modules/navier_stokes/test/tests/finite_volume/wcns/materials/gold/1d_test_cpT_out.csv
@@ -0,0 +1,3 @@
+time,H_in,H_out,Q,T_analytical,T_out,balance_in_percent,error_T
+0,0,0,1500000,899.2226858156,0,0,0
+1,-24665522.4,26165522.540111,1500000,899.2226858156,899.22268943977,-5.6804577370916e-07,3.6241718817109e-06
diff --git a/modules/navier_stokes/test/tests/finite_volume/wcns/materials/tests b/modules/navier_stokes/test/tests/finite_volume/wcns/materials/tests
index 95d669f960f7..66c7292a6f5c 100644
--- a/modules/navier_stokes/test/tests/finite_volume/wcns/materials/tests
+++ b/modules/navier_stokes/test/tests/finite_volume/wcns/materials/tests
@@ -57,6 +57,13 @@
     requirement = 'The system shall be able to compute the specific enthalpy and the enthalpy with a non constant specific heat.'
     recover = false
   []
+  [validation_nonconstant_cp]
+    type = 'CSVDiff'
+    input = 1d_test_cpT.i
+    csvdiff = 1d_test_cpT_out.csv
+    requirement = 'The system shall be able to compute the specific enthalpy and the enthalpy with a non constant specific heat, and show near perfect energy conservation.'
+    recover = false
+  []
 
   [exceptions]
     requirement = "The system shall throw an error if"