[LeegleechN]

The molecules in a crystal still vibrate kinetically. A solid with no molecular motion would be at absolute zero temperature.

[aeonik]

Wouldn't a fair amount of the thermal energy be hanging out in the bonds themselves? The stress in the system has to count for something.

I'm imagining a bunch of potential energy being stored in the fields at any given moment.

[ivalm]

Absolutely, but that’s not heat. Things like heat produced from burning wood is an example of potential energy of binds getting released as kinetic energy + photons.