  The analytic expressions for the free energy and entropy of the
Casimir-Polder interaction between a polarizable and magnetizable atom and a
graphene sheet are found in the limiting case of low temperature. In so doing,
the response of graphene to electromagnetic fluctuations is described in the
framework of the Dirac model by means of the polarization tensor in
(2+1)-dimensional space-time. It is shown that the dominant contribution to the
low-temperature behavior is given by an explicit dependence of the polarization
tensor on temperature as a parameter. We demonstrate that the Lifshitz theory
of atom-graphene interaction satisfies the Nernst heat theorem, i.e., is
thermodynamically consistent. On this basis possible reasons of thermodynamic
inconsistency arising for the Casimir-Polder and Casimir interactions in the
case of Drude metals are discussed. The conclusion is made that although large
thermal effect arising in the Casimir interaction between Drude metals at short
separations should be considered as an artifact, the giant thermal effect
predicted for graphene systems is an important physical phenomenon which awaits
for its experimental observation.
