Abstract We study a two-component bistable reaction-diffusion system arising in a model for a simple reversible chemical reaction subject to the effect of thermal activation and energy production and dissipation. Some mathematical simplications enables the analytical resolution of the corresponding reaction-diffusion equation set in a variety of situations. As a first step, we analyze the evolution of the system in spatially homogeneous conditions. This makes it possible to detect the parameter regions where bistability occurs, identifying the physical conditions under which two stable states exist. Then, we study shape-preserving wave-front solutions. These fronts should stand for the motion of domain walls, formed during the self-organizing stage of the evolution.