When two bodies of matter are placed together, one hotter than the other, where does the energy go when the two temperatures equalize?
Is there any energy in thermal difference at all? If not, how else does the thermoelectric effect work?
In a solid body the energy that we call heat is stored as vibrational motion of the atoms/molecules in the solid. When you place a hot solid in contact with a cold one the vibrating atoms in the hot solid bash into the more slowly vibrating atoms of the cold solid and transfer energy to them. You end up with the atoms in the hot body vibrating a bit less and the atoms in the cold body vibrating a bit more.
The thermoelectric effect arises by a different mechanism. In materials with mobile electrons (i.e. principally metals, but also semiconductors) the electron energy depends on temperature and electrons will diffuse from a hot region to a cold one. This generates a potential difference.