Check out Kittel - the basic bible of solid state physics.  But to
give a short explanation, thermal energy added to a single atom will
be just like any other form of EM energy added to a photon - the
electron will eventually jump to a higher orbital and fall back,
releasing an acoustic phonon to the crystal lattice instead of an
electron - that is, if the material is not a direct gap semiconductor.

Important things to realize, for coupled vibrations (e.g. crystal
lattice, the basic model starts out with coupled oscillators, look at
the derivations in Kittel) you have the coupled oscillator model.

As far as the nucleus moving, that's not the case except that the
entire atom will move in sympathetic vibration (e.g. when acoustic
waves propagate through the material with phonons).

-EricW