We study the thermal propagation of a reaction wave through a condensed medium in the case when the thermal conductivity of the mixture may change in a jumpwise fashion at some critical temperature. This can occur, e.g., when the actual heat transfer processes are accounted for as a heat conduction process with an effective thermal conductivity. Then a change in the actual mechanism of heat transfer at some point in the reaction wave may result in a significantly different effective thermal conductivity. Our model also allows for the thermal conductivity of the product to be different from that for the initial reactants. We have determined the structure of uniformly propagating reaction waves and analyzed their stability. We have shown, in particular, that if the thermal conductivity is increased in a region just ahead of the reaction zone then the wave is either stabilized on destabilized depending on whether the width of this region is below or above a critical value.