diff --git a/src/materials/heat_conductivity.jl b/src/materials/heat_conductivity.jl
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+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+"""
+Linear isotropic heat-conductivity material model.
+
+Mirror image of `LinearElastic` for the heat-conduction physics. The
+constitutive law is Fourier's law
+
+    q = -k · ∇T,        ∂q/∂(∇T) = -k · I
+
+so the per-IP "tangent" we cache is the (constant, isotropic) symmetric
+2nd-order tensor `k * I`. Anisotropic / temperature-dependent
+conductivities are intentionally out of scope; they reuse the same
+microkernel contract by replacing this struct.
+"""
+
+using Tensors
+
+"""
+    HeatConductivity <: AbstractMaterial
+
+Linear isotropic heat-conductivity material.
+
+# Fields
+- `k::Float64` — thermal conductivity [W / (m·K)]; must be positive.
+
+# Example
+```julia
+copper = HeatConductivity(k = 401.0)
+steel  = HeatConductivity(k = 50.2)
+```
+"""
+struct HeatConductivity <: AbstractMaterial
+    k::Float64
+
+    function HeatConductivity(k::Float64)
+        k > 0.0 || throw(ArgumentError("Thermal conductivity k must be positive, got k = $k"))
+        new(k)
+    end
+end
+
+"""
+    HeatConductivity(; k)
+
+Convenience constructor with keyword argument.
+"""
+HeatConductivity(; k) = HeatConductivity(Float64(k))
+
+# ---------- Trait declarations ----------------------------------------------
+
+material_behavior(::HeatConductivity) = StatelessConstantTangent()
+supported_physics(::HeatConductivity) = (Thermal{3}(),)
+required_state_variables(::HeatConductivity) = ()
+
+# ---------- Constitutive law ------------------------------------------------
+
+"""
+    conductivity_tensor(material::HeatConductivity) -> SymmetricTensor{2,3,Float64,6}
+
+Return the (constant, isotropic) conductivity 2nd-order tensor `k · I`.
+This is what each IP sees through the heat microkernel buffer.
+"""
+@inline function conductivity_tensor(material::HeatConductivity)
+    return material.k * one(SymmetricTensor{2,3,Float64,6})
+end
+
+"""
+    scalar_diffusion_tensor(material::HeatConductivity)
+
+Symmetric positive-definite tensor `k` in the weak form
+`∫ ∇v · k · ∇u dV` used by [`HeatKernel`](@ref). Identical to
+[`conductivity_tensor`](@ref); the name is shared with
+[`HydraulicConductivity`](@ref) for primal flow-potential problems.
+"""
+@inline scalar_diffusion_tensor(material::HeatConductivity) = conductivity_tensor(material)
+
+"""
+    compute_heat_flux(material::HeatConductivity, ∇T, state_old, Δt)
+        -> (q, K, state_new)
+
+Heat-conduction analogue of `compute_stress`:
+
+* `material::HeatConductivity` — material model
+* `∇T::Vec{3,Float64}`         — temperature gradient at the current IP
+* `state_old`                  — previous-step state (`nothing` /
+  `NamedTuple()` for stateless conductivity)
+* `Δt::Float64`                — time increment
+
+Returns `(q, K, state_new)` where
+
+* `q::Vec{3,Float64}`                          — heat flux `q = -k·∇T`
+* `K::SymmetricTensor{2,3,Float64,6}`          — conductivity `k·I`,
+  the constant symmetric tangent `∂q/∂(∇T) = -K` (sign convention:
+  positive-definite K so the stiffness `Bᵀ K B` is SPD)
+* `state_new::NamedTuple`                      — empty NamedTuple
+  (stateless material)
+"""
+function compute_heat_flux(
+    material::HeatConductivity,
+    ∇T::Vec{3,T},
+    state_old::Union{Nothing,NamedTuple},
+    Δt::Float64,
+) where T
+    K = conductivity_tensor(material)
+    q = -K ⋅ ∇T
+    return q, K, NamedTuple()
+end
+
+compute_heat_flux(material::HeatConductivity, ∇T::Vec{3,T}) where T =
+    compute_heat_flux(material, ∇T, nothing, 0.0)