  The thermal correction to the energy of Casimir-Polder interaction of atoms
with a suspended graphene membrane described by the Dirac model is
investigated. We show that a major impact on the thermal correction is made by
the size of the gap in the energy spectrum of graphene quasiparticles.
Specifically, if the temperature is much smaller than the gap parameter
(alternatively, larger or of the order of the gap parameter), the thermal
correction is shown to be relatively small (alternatively, large). We have
calculated the free energy of the thermal Casimir-Polder interaction of atoms
of He, Na, Rb, and Cs with graphene described by both the hydrodynamic and
Dirac models. It is shown that in exact computations using the Dirac model, one
should use the polarization operator at nonzero temperature. The computational
results for the Casimir-Polder free energy obtained in the framework of
hydrodynamic model of graphene are several times larger than in the Dirac model
within the separation region below 2$\mu$m. We conclude that the theoretical
predictions following from the two models can be reliably discriminated in
experiments on quantum reflection of different atoms on graphene.
