  The Casimir interaction between two thick parallel plates, one made of metal
and the other of dielectric, is investigated at nonzero temperature. It is
shown that in some temperature intervals the Casimir pressure and the free
energy of a fluctuating field are the nonmonotonous functions of temperature
and the respective Casimir entropy can be negative. The physical interpretation
for these conclusions is given. At the same time we demonstrate that the
entropy vanishes when the temperature goes to zero, i.e., in the Casimir
interaction between metal and dielectric the Nernst heat theorem is satisfied.
The investigation is performed both analytically, by using the model of an
ideal metal and dilute dielectric or dielectric with a frequency-independent
dielectric permittivity, and numerically for real metal (Au) and dielectrics
with different behavior of the dielectric permittivity along the imaginary
frequency axis (Si and Al_2O_3).
