This work studies the heat equation in a two-phase material with spherical inclusions.
Under some appropriate scaling on the size, volume fraction and heat capacity of the
inclusions, we derive a coupled system of partial differential equations governing the
evolution of the temperature of each phase at a macroscopic level of description. The
coupling terms describing the exchange of heat between the phases are obtained by using
homogenization techniques originating from [D. Cioranescu, F. Murat, Collège de France
Seminar, vol. II. Paris 1979–1980; vol. 60 of Res. Notes Math. Pitman,
Boston, London (1982) 98–138].