Fourier's law ($\mathbf{q}=-k\nabla T$)

Fourier's law relates the conductive heat-flux density $\mathbf{q}$ to the temperature gradient by $\mathbf{q}=-k\nabla T$.

Thermal conductivity is the positive material coefficient $k$ in Fourier's law. It may depend on temperature, composition, and direction.

Thermal diffusivity is $\kappa =k/(\rho c_p)$, the ratio of thermal conductivity to volumetric heat capacity. It sets the diffusion length $\sqrt{\kappa t}$ over time $t$.