This article considers an exothermic chemical reaction taking place in a stockpile of reactive material with a thermal conductivity that is temperature dependent. The study is modeled in a spherical domain whose carbon-containing material reacts spontaneously with the oxygen trapped within the system. The combustion process results with a complicated process that is nonlinear in nature, and the energy equation used to govern the problem is tackled numerically with the semi-implicit finite difference method (FDM). The results are depicted graphically and discussed to give a theoretical understanding of the heat transfer analysis during combustion. © Published under licence by IOP Publishing Ltd.