  We study the Hamiltonian system made of weakly coupled anharmonic oscillators
arranged on a three dimensional lattice and subjected to a stochastic forcing
mimicking heat baths of temperatures T_1 and T_2 on the hyperplanes at x_1=0
and N. We introduce a truncation of the Hopf equations describing the
stationary state of the system which leads to a nonlinear equation for the
two-point stationary correlation functions. We prove that these equations have
a unique solution which, for N large, is approximately a local equlibrium state
satisfying Fourier law that relates the heat current to a local temperature
gradient. The temperature exhibits a nonlinear profile.
