  We compute the first-order correction to the correlation functions of the
stationary state of a stochastically forced harmonic chain out of equilibrium
when a small on-site anharmonic potential is added. This is achieved by
deriving a suitable formula for the covariance matrix of the invariant state.
We find that the first-order correction of the heat current does not depend on
the size of the system. Second, the temperature profile is linear when the
harmonic part of the on-site potential is zero. The sign of the gradient of the
profile, however, is opposite to the sign of the temperature difference of the
two heat baths.
