We formulate and investigate a uniformly distributed mathematical model (based upon Semenov's theory for thermal explosions) for the thermal response of cellulosic materials in compost piles. The model consists of a mass balance equation for oxygen, a heat balance equation, and incorporates the heat release due to biological activity within the pile. Biological heat generation is known to be present in most industrial processes handling large volumes of bulk organic materials. We utilise singularity theory to investigate the generic properties of the model, as well as to determine the locus of different singularities, namely the cusp, isola and double limit point. Singularity theory provides a useful tool to systematically analyse this system. We investigate the conditions where biological activity results in the initiation of an elevated temperature branch within the compost pile.