  We study the zero and finite temperature Casimir force acting on a perfectly
conducting piston with arbitrary cross section moving inside a closed cylinder
with infinitely permeable walls. We show that at any temperature, the Casimir
force always tends to move the piston away from the walls and towards its
equilibrium position. In the case of rectangular piston, exact expressions for
the Casimir force are derived. In the high temperature regime, we show that the
leading term of the Casimir force is linear in temperature and therefore the
Casimir force has a classical limit. Due to duality, all these result also hold
for an infinitely permeable piston moving inside a closed cylinder with
perfectly conducting walls.
