This paper is motivated by a model for the injection of air into an underground porous medium that contains a solid fuel, taking into account thermal losses to the surrounding rock. In our previous works the model
was simplified and all wave sequences for the Riemann problem solution were
obtained. Additionally, a rigorous proof of the existence of the traveling wave solution was presented. Taking thermal losses into account is important from a physical point of view because they play an important role, especially in the laboratory experiments.

In this work the first step is made to understand the effect of heat losses. The
model is modified by including the thermal losses term, making it more physically realistic. In order to simplify the proof of the existence and uniqueness of the traveling wave solution, we disregard diffusion effects and the dependence of gas density on temperature. Some numerical examples are presented to illustrate the theoretical study.