The motion depends on the external potential that the atom is sitting in. In field free space (constant potential) it will just translate at constant velocity. In a harmonic potential, it will oscillate sinusoidally about a mean position.
For the most part this is all that happens - there are no significant changes at the subatomic level.
How do atoms transfer KE to one another ? ...through the coulomb interaction between the charged components of the atoms (the nucleii and electrons).