This paper describes a methodology developed to perform electro-thermal analysis of integrated circuits. This method is based on the relaxation approach. A circuit simulator and a thermal simulator which is a finite element program are coupled by an interface program. This method is applied to perform electro-thermal analysis of Si bipolar junction transistor (BJT) to predict the temperature distribution and the device performance in a circuit. Thermal non-linearity due to temperature-dependent material parameters in the context of thermal modeling of device and circuit has been considered. The simulation results indicate a temperature increase of device when biased in a moderate operating point. The junction temperature was about 107.2 degC at a power dissipation of 4.5 W