A new approach to the analysis of large-scale thermal system has been developed, in which the thermal resistance matrix of principal portions of the system can be computed very quickly. The features of this method are 1) approximation of rectangular heat sources by equivalent circular ones, 2) formulation of a thermal equation under condition that the semiconductor chip extends infinitely, and 3) modification for a finite chip using the image method, upon necessity. In this paper, formulation and discussions of the present method are described with applications to the thermal problems for high-frequency power transistors that are divided in a large number of cellular devices. Using the present method, isothermal design and thermal instability phenomena such as hot spots and current crowdings are studied.