  We investigate a one dimensional chain of $2N$ harmonic oscillators in which
neighboring sites have their energies redistributed randomly. The sites $-N$
and $N$ are in contact with thermal reservoirs at different temperature
$\tau_-$ and $\tau_+$. Kipnis, Marchioro, and Presutti \cite{KMP} proved that
this model satisfies {}Fourier's law and that in the hydrodynamical scaling
limit, when $N \to \infty$, the stationary state has a linear energy density
profile $\bar \theta(u)$, $u \in [-1,1]$. We derive the large deviation
function $S(\theta(u))$ for the probability of finding, in the stationary
state, a profile $\theta(u)$ different from $\bar \theta(u)$. The function
$S(\theta)$ has striking similarities to, but also large differences from, the
corresponding one of the symmetric exclusion process. Like the latter it is
nonlocal and satisfies a variational equation. Unlike the latter it is not
convex and the Gaussian normal fluctuations are enhanced rather than suppressed
compared to the local equilibrium state. We also briefly discuss more general
model and find the features common in these two and other models whose
$S(\theta)$ is known.

Statistical Mechanics