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We study a one-dimensional hamiltonian chain of masses perturbed by an energyconserving noise. The dynamics is such that, according to its hamiltonian part,particles move freely in cells and interact with their neighbors throughcollisions, made possible by a small overlap of size $\epsilon > 0$ betweennear cells. The noise only randomly flips the velocity of the particles. If$\epsilon \rightarrow 0$, and if time is rescaled by a factor $1/{\epsilon}$,we show that energy evolves autonomously according to a stochastic equation,which hydrodynamic limit is known in some cases. In particular, if only twodifferent energies are present, the limiting process coincides with the simplesymmetric exclusion process.

Energy transport through rare collisions