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Aren't they both caused by electron motion?

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Related: – Kitchi Oct 14 '13 at 10:24

Thermal conductivity relates to the propagation of heat, whereas electrical conductivity relates to the effective propagation of electric charge.

In the case of thermal conductivity, not only the electrons play a role in the conduction but also phonons or magnons contribute to it. The electrons only play a significant role in heat conductivity in metallic materials, where you have relatively free electrons available.

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And that is why in general materials with high electrical conductivity also have high thermal conductivity. In fact for metals the two conductivities are related by the Wiedemann-Franz Law which says

\begin{equation} \frac{k}{\sigma}=LT \end{equation}

More details can be found here

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