Cluster expansions are simplified, Ising-like models for binary alloys in which vibrational and electronic degrees of freedom are coarse grained. The usual practice is to learn the parameters of the cluster expansion by fitting the energy they predict to a finite set of ab initio calculations. In some cases, experiments suggest that such approaches may lead to overestimation of the phase transition temperature. In this work, we present a novel approach to fitting the parameters based on the relative entropy framework which, instead of energies, attempts to fit the Boltzmann distribution of the configurational degrees of freedom. We show how this leads to T-dependent parameters.