The development of a three-dimensional thermal mathematical model of a pellistor based on the fundamental physical laws of heat transfer and employing a few clearly stated simplifying assumptions concerning the convective heat transfer in ambient air is reported. The model was numerically solved using the implicit alternating-direction finite difference method. The software was written in Microsoft and Gnu C and run on a PC. Simulations for studying the transient heat transfer in the absence of flammable gas were performed. Refinement of the model in terms of reducing the simplifying assumptions and the experimental verification of the simulated thermal behaviour of the model structure is in progress. In its final form the model should be capable of describing more sophisticated micro-pellistor structures.