  In this paper we consider a superconducting film modeled by the
Ginzburg-Landau model, confined between two parallel planes a distance $L$
apart from one another. Our approach is based on the Gaussian effective
potential in the transverse unitarity gauge, which allows to treat gauge
contributions in a compact form. Using techniques from dimensional and
$zeta$-function regularizations, modified by the confinement conditions, we
investigate the critical temperature as a function of the film thickness $L$.
The contributions from the scalar self-interaction and from the gauge
fluctuations are clearly identified. The model suggests the existence of a
minimal critical thickness below which superconductivity is suppressed.
