  We demonstrate that Casimir-Polder potentials can be entirely independent of
temperature even when allowing for the thermal photon numbers to become large
at the relevant molecular transition frequencies. This statement holds for
potentials that are due to low-energy transitions of a molecule placed near a
plane metal surface. For a molecule in an energy eigenstate, the
temperature-invariance is a consequence of strong cancellations between
nonresonant potential components and those due to evanescent waves. For a
molecule with a single dominant transition in a thermal state, upward and
downward transitions combine to a temperature-independent potential. The
results are contrasted with the case of an atom whose potential exhibits a
regime of linear temperature-dependence. Contact to the Casimir force between a
weakly dielectric and a metal plate is made.
