We consider the combustion, in a gravitational field, of a heterogeneous powder mixture compressed into a solid sample, in which the high temperature ahead of the reaction zone destroys the solid, due, e.g. to melting of some of components of the mixture. Thus, a suspension is formed, consisting of a liquid bath containing solid or liquid particles. Processes such as hear and mass transfer as well as chemical reactions in the suspension determine the structure of the combustion wave and its propagation velocity. Under the influence of gravitational forces there is the possibility of relative motion of the liquid and solid. Previous theoretical analyses considered the rate of heat transfer between the solid and liquid phases to be sufficiently large that their two distinct temperatures rapidly equilibrated to a single temperature. In addition to this case, we also consider the case when the rate of heat transfer is not so large and the model involves the separate temperatures of the solid and liquid phases. We Fmd that multiplicity of traveling wave structures is possible. In particular, in addition to a low velocity structure, which is essentially the same as that obtained from the one temperature description, we find a high velocity structure, which does not exist in the one temperature description, but rather depends on the fact that the solid and fluid temperatures differ from each other. Both structures can exist for the same parameter values in a given range. We describe the dependence of the combustion characteristics of the two structures on gravitational forces and other factors. In particular, we compare the characteristics in gravity and microgravity environments.