Earth’s crust is an anisotropic and purely heterogeneous medium, which is justified by existence of different discontinuities, our study aims to show the effect of the variation of coefficient of friction on the evolution of temperature and its impact on seismic forecasting. In this work, we are model in 2D the variation of thermal energy and temperature produced by friction at the level of fault lip as function of depth of the seismic focus and at different value of time. Earthquakes are born when the energy accumulated by friction at the level of fault is suddenly released causing damage, sometimes noticeable on the surface of earth (macroseisms), and sometimes not at all noticeable on the surface of earth (microseisms), then energy which occurs before is important to forecasting earthquake. Assuming that coefficient of friction is variable, our results have enabled us to highlight the fact that, the greater the coefficient of friction, more the temperature increases, although the temperature profile increase over time but not linearly reflecting the presence of different asperities and discontinuities zone; slip generated at the level of fault occur a variation of temperature on specific points called roughness in common agreement with the literature. A large part of energy produced by friction is dissipated in heat causing a local increases in temperature which a very short duration and called flash contact temperature, and that despite the fact that the temperature evolved in time and space, it all converged towards a perfectly distinguishable fixed point. In this draft article, we model by mains of mathematical expressions, the thermal energy produced by friction at the level of the lip of fault as well as the variation of the temperature occurs by friction at the level of the lip of fault by admitting the variation of coefficient of friction. The results which we obtained are interesting and especially carrying the object of a publication. We showed in this work that : Slip generated at the level of fault occur a variation of temperature on specific points called asperity. 1 Beyond a certain value of the depth of the seismic focus, the variation of the temperature produced by friction is null. Temperature and energy profiles obtained following the variation of the friction coefficient reveals heterogeneous character of earth crust’s.