  We study the error of the Euler scheme applied to a stochastic partial
differential equation. We prove that as it is often the case, the weak order of
convergence is twice the strong order. A key ingredient in our proof is
Malliavin calculus which enables us to get rid of the irregular terms of the
error. We apply our method to the case a semilinear stochastic heat equation
driven by a space-time white noise.
