Thermal stability of reactive materials in a stockpile which spontaneously ignites is investigated in this article. The stockpile is modeled in a spherical domain assumed to be of a constant thermal conductivity. The energy equation is modified to a partial differential equation that is most suitable to analyze thermal stability of the combusting material. This is carried out by looking at the behavior of the temperature as selected parameters embedded in the governing equation are varied. The governing equation is solved numerically by using the Finite Difference Method (FDM). The results are given graphically and discussed appropriately to provide an understanding of the complicated combustion process. © 2018 Faculty of Engineering, Alexandria University