  In the context of the Ginzburg--Landau theory for critical phenomena, we
consider the Euclidean $\lambda \phi ^4+\eta \phi^6$ model bounded by two
parallel planes, a distance $L$ separating them. This is supposed to describe a
sample of a superconducting material undergoing a first-order phase transition.
We are able to determine the dependence of the transition temperature $T_{c}$
for the system as a function of $L$. We show that $% T_{c}(L)$ is a concave
function of $L$, in qualitative accordance with some experimental results. The
form of this function is rather different from the corresponding one for a
second-order transition.
