  We study the BCS critical temperature on half-spaces in dimensions $d=1,2,3$
with Dirichlet or Neumann boundary conditions. We prove that the critical
temperature on a half-space is strictly higher than on $\mathbb{R}^d$, at least
at weak coupling in $d=1,2$ and weak coupling and small chemical potential in
$d=3$. Furthermore, we show that the relative shift in critical temperature
vanishes in the weak coupling limit.
