  We evaluate the difference between the Casimir free energies corresponding to
either grounded or isolated perfect conductors, at high temperatures. We show
that a general and simple expression for that difference can be given, in terms
of the electrostatic capacitance matrix for the system of conductors. For the
case of close conductors, we provide approximate expressions for that
difference, by evaluating the capacitance matrix using the proximity force
approximation. Since the high-temperature limit for the Casimir free energy for
a medium described by a frequency-dependent conductivity diverging at zero
frequency coincides with that of an isolated conductor, our results may shed
light on the corrections to the Casimir force in the presence of real
materials.
