Motors and appliances get hot because inefficiencies eventually become waste heat. That is the source of the heat. It propagates from tbe heat source to a surface you can feel through conduction and other mechanisms.

Thanks!

Motors become hot because they generate heat through friction and other forms of loss. Many other appliances generate heat this way (and some are designed to generate heat).

Conductive materials are likely to be good heat conductors because the electrons themselves can conduct heat, and because the crystal structures of conventional metals (e.g. copper) tend to be good for both.

These two effects are entirely unrelated.

Thanks, that makes sense.

The relationship is generally true for metals (https://en.wikipedia.org/wiki/Wiedemann–Franz_law) but an appliance being warm to the touch because you use it is not really related.