  A process based on the exactly solvable Kipnis--Marchioro--Presutti model of
heat conduction [J. Stat. Phys. 27 65 (1982)] is described whereby lattice
cells share their energies among many identical degrees of freedom while, in
each cell, only two of them are associated with energy exchanges connecting
neighbouring cells. It is shown that, up to dimensional constants, the heat
conductivity is half the interaction rate, regardless of the degrees of
freedom. Moreover, as this number becomes large, correlations between the
energy variables involved in the exchanges vanish. In this regime, the process
thus boils down to the time-evolution of the local temperatures which is
prescribed by the discrete heat equation.
