  We consider a continuous analogue of the simulated annealing algorithm in
$R^d$. We prove a convergence result, under hypotheses weaker than the usual
ones. In particular, we cover cases where the gradient of the potential goes to
zero at infinity. The proof follows an idea of L. Miclo, but we replace the
Poincar\'e and log-Sobolev inequalities (which do not hold in our setting) by
weak Poincar\'e inequalities. We estimate the latter with measure-capacity
criteria. We show that, despite the absence of a spectral gap, the convergence
still holds for the "classical" schedule t = c/ ln(t), if c is bigger than a
constant related to the potential.
