In this study, unsteady heat transfer problem has been solved to calculate the temperature distribution of a machine gun barrel. Time dependent convective heat transfer coefficient to predict the entire wall temperature of the barrel wall has been calculated by means of internal ballistic theory. The numerical solution of the differential equation was carried out by means of finite difference method. Thermal characteristics of the gun barrel material are considered to be temperature dependent. The study is extended also to cover the multi shot ballistic cycle, such that it would be possible to obtain the cook-off temperature of the gun. The numerical results are compared with the experimental results found in literature. The agreement between them is quite satisfactory.