We examine the reaction fronts that develop when an undersaturated ‘injection fluid’ displaces a saturated ‘formation fluid’ in a chemically reactive porous medium. We allow the injection and formation fluids to differ both in temperature and in chemical composition. The undersaturation of the incoming fluid drives a dissolution reaction and leads to the formation of a ‘depletion’ front. Under certain circumstances, which we describe, the temperature difference drives a separate thermal reaction front. We develop long-time asymptotic solutions of the governing equations which illustrate the interaction between thermal reaction fronts and depletion fronts. Two distinct regimes arise. If the compositional difference between the injection and formation fluids exceeds a critical value, the depletion front travels faster than the thermal front, leaving the porous medium depleted of reactant from the source to a point downstream of the thermal front and no thermal reaction front develops. Conversely, if the compositional difference is smaller than the critical value, a thermal reaction front advances ahead of the depletion front and so there is a double reaction front structure. We illustrate the evolution of the thermal and compositional fields towards these asymptotic solutions with numerical simulations. We discuss the implications of this work for secondary mineralization in subsurface reservoirs.