We consider the self heating process in a two dimensional spatially dependent model of a compost pile which incorporates terms that account for self heating due to both biological and oxidation mechanisms. As moisture is a crucial factor in both the degradation process and spontaneous ignition within a compost pile, this model consists of four mass-balance equations, namely, energy, oxygen, vapour and liquid water concentrations. Analyses are undertaken for different initial water contents within the compost pile. We show that when the water content is too low, the reaction is almost negligible; whereas when it is too high, the reaction commences only when the water content evaporates and the water ratio drops to within an appropriate range. However, for an intermediate water content range, the biological reaction is at its optimum and there is a possibility of spontaneous ignition within the compost pile. © Austral. Mathematical Soc. 2012.