This paper considers the self-heating process occurring in a compost pile using one- and two-dimensional spatially-dependent models and incorporating terms that account for self-heating due to both biological and oxidative mechanisms. Biological heat generation is known to be present in most industrial processes handling large volumes of bulk organic materials. The heat release rate due to biological activity is modelled by a function which is, at sufficiently low temperatures, a monotonically increasing function of temperature and, at higher temperatures, a monotonically decreasing function of temperature. This functionality represents the fact that microorganisms die or become dormant at high temperatures. The heat release rate due to oxidation reactions is modelled by Arrhenius kinetics. As moisture is another crucial factor in the degradation process of compost, 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, for the case when the water content is too high, the reaction only commences when the water content evaporates and the water ratio drops into an appropriate range. However, for an intermediate water content range, biological reaction is at its optimum and there is a possibility of spontaneous combustion of the compost pile.