In this paper we model the thermal behaviour of compost heaps in the presence of micro-organism undergoing oxidative exothermic reactions. For simplicity we consider a spatially uniform model in which oxidative reactions of the cellulosic components is ignored. We use singularity theory to investigate the generic properties of the model. We show that there are two generic steady-state diagrams including one in which the temperature-response curve is the standard S-shaped curve familiar from combustion problems. Such a steady-state diagram contains an elevated temperature branch, which is the feature of practical interest in facilities such as industrial compost heaps and municipal tips. Thus biological self-heating can cause jumps in the steady-temperature. We outline a procedure by which reasonable values of the kinetic parameters can be estimated.