  We investigate the thermal Casimir interaction of a suspended graphene
described by the Dirac model with a plate made of dielectric or metallic
materials. The reflection coefficients on graphene expressed in terms of a
temperature-dependent polarization tensor are used. We demonstrate that for a
graphene with nonzero mass gap parameter the Casimir free energy remains nearly
constant (and the thermal correction negligibly small) over some temperature
interval. For the interaction of graphene with metallic plate, the free energy
is nearly the same, irrespective of whether the metal is nonmagnetic or
magnetic and whether it is described using the Drude- or plasma-model
approaches. The free energy computed using the Dirac model was compared with
that computed using the hydrodynamic model of graphene and big differences
accessible for experimental observation have been found. For dielectric and
nonmagnetic metallic plates described by the Drude model these differences
vanish with increasing temperature (separation). However, for nonmagnetic
metals described by the plasma model and for magnetic metals, a severe
dependence on the chosen theoretical description of graphene remains even at
high temperature. In all cases the analytic asymptotic expressions for the free
energy at high temperature are obtained and found in a very good agreement with
the results of numerical computations.
