  We review recent results obtained in the physics of the thermal Casimir force
acting between two dielectrics, dielectric and metal, and between metal and
semiconductor. The detailed derivation for the low-temperature behavior of the
Casimir free energy, pressure and entropy in the configuration of two real
dielectric plates is presented. For dielectrics with finite static dielectric
permittivity it is shown that the Nernst heat theorem is satisfied. Hence, the
Lifshitz theory of the van der Waals and Casimir forces is demonstrated to be
consistent with thermodynamics. The nonzero dc conductivity of dielectric
plates is proved to lead to a violation of the Nernst heat theorem and, thus,
is not related to the phenomenon of dispersion forces. The low-temperature
asymptotics of the Casimir free energy, pressure and entropy are derived also
in the configuration of one metal and one dielectric plate. The results are
shown to be consistent with thermodynamics if the dielectric plate possesses a
finite static dielectric permittivity. If the dc conductivity of a dielectric
plate is taken into account this results in the violation of the Nernst heat
theorem. We discuss both the experimental and theoretical results related to
the Casimir interaction between metal and semiconductor with different charge
carrier density. Discussions in the literature on the possible influence of
spatial dispersion on the thermal Casimir force are analyzed. In conclusion,
the conventional Lifshitz theory taking into account only the frequency
dispersion remains the reliable foundation for the interpretation of all
present experiments.
