  We use a functional approach to evaluate the Casimir free energy for a
self-interacting scalar field in $d+1$ dimensions, satisfying Dirichlet
boundary conditions on two parallel planes. When the interaction is turned off,
exact results for the free energy in some particular cases may be found, as
well as low and high temperature expansions based on a duality relation that
involves the inverse temperature $\beta$ and the distance between the mirrors,
$a$. For the interacting theory, we derive and implement two different
approaches. The first one is a perturbative expansion built with a thermal
propagator that satisfies Dirichlet boundary conditions on the mirrors. The
second approach uses the exact finite-temperature generating functional as a
starting point. In this sense, it allows one to include, for example,
non-perturbative thermal corrections into the Casimir calculation, in a
controlled way. We present results for calculations performed using those two
approaches.
