  We consider a bounded open Stein subset $\Omega$ of a complex Stein manifold
$X$ of dimension $n$. We prove that if $f$ is a current on $X$ of bidegree
$(p,q+1)$, $\bar\partial$-closed on $\Omega$, we can find a current $u$ on $X$
of bidegree $(p,q)$ which is a solution of the equation $\bar\partial u=f$ in
$\Omega$. In other words, we prove that the Dolbeault complex of temperate
currents on $\Omega$ (i.e. currents on $\Omega$ which extend to currents on
$X$) is concentrated in degree $0$. Moreover if $f$ is a current on $X= C^n$ of
order $k$, then we can find a solution $u$ which is a current on $C^n$ of order
$k+2n+1$.
