In this article, we consider thermal stability and oxygen consumption rate in a reactive stockpile material and at the same time spontaneously combusts. Spontaneous combustion usually takes place when a material containing carbon or hydrocarbon reacts with oxygen that is trapped within the stockpile due to low-temperature oxidation. Heat is one of the products of combustion in any exothermic chemical reaction, and in this case, complete combustion is assumed with the reactant oxygen consumption. The study is done theoretically with the application of energy and mass transfer equations, to give an understanding of the complicated process of combustion. The nonlinear differential equations governing the problem are solved numerically using semi-implicit finite difference method (FDM). The reactant and the temperature behaviors are depicted graphically, and results are discussed accordingly. © 2017 Praise Worthy Prize S.r.l. All rights reserved.