Material properties such as thermal conductivity can depend on temperature. The actual calculation of thermal conductivity of various materials is very much outside of my area, but Schroeder’s “An Introduction to Thermal Physics” has a somewhat similar derivation showing the thermal conductivity of an ideal gas being proportional to √T based off the rms velocity and mean free path (which can be related to average time between collisions).
Material properties such as thermal conductivity can depend on temperature. The actual calculation of thermal conductivity of various materials is very much outside of my area, but Schroeder’s “An Introduction to Thermal Physics” has a somewhat similar derivation showing the thermal conductivity of an ideal gas being proportional to √T based off the rms velocity and mean free path (which can be related to average time between collisions).