  We consider a model for thermal contact through a diathermal interface
between two macroscopic bodies at different temperatures: an Ising spin chain
with nearest neighbor interactions is endowed with a Glauber dynamics with
different temperatures and kinetic parameters on alternating sites. The
inhomogeneity of the kinetic parameter is a novelty with respect to the model
of Ref.[1] and we exhibit its influence upon the stationary non equilibrium
values of the two-spin correlations at any distance. By mapping to the dynamics
of spin domain walls and using free fermion techniques, we determine the scaled
generating function for the cumulants of the exchanged heat amounts per unit of
time in the long time limit.
