  Different non-equilibrium situations have recently been considered when
studying the thermal Casimir--Polder interaction with a body. We show that the
Keldysh Green function method provides a very general common framework for such
studies where non-equilibrium of either the atom or the body with the
environment can be accounted for. We apply the results to the case of ground
state polar molecules out of equilibrium with their environment, observing
several striking effects. We consider thermal Casimir--Polder potentials in
planar configurations, and new results for a molecule in a cylindrical cavity
are reported, showing similar characteristic behaviour as found in planar
geometry.
