Summary: We analyze the microwave heating of a ceramic composite which consists of small ceramic particles embedded in a ceramic cement. The composite is well insulated, and each particle is in imperfect thermal contact with the surrounding cement. Based on these two assumptions, we develop an asymptotic theory exploiting the small Biot number and small non-dimensional contact conductance. Our asymptotic theory yields a set of nonlinear partial differential equations which govern the temperature in the composite. These are reduced to a set of coupled nonlinear ordinary differential equations in which the surface area of each particle enters as a parameter. Recent experiments with such composites have shown that the steady-state temperature of the composite is strongly dependent upon the radii of embedded particles. Our model captures this effect. In fact, our analysis shows that the assumption of imperfect thermal contact between the particles and the ceramic cement is essential for this trend to be established.