Due to downsizing of the ICs and to increasing density of packaging, the importance of on-line temperature monitoring and distribution in hybrid circuits is ever increasing. The analysis of heat distribution mechanism in hybrid circuits has been carried out and a mathematical model For circuits with multi-layer substrate has been detailed. A computer program was written to perform steady-state analysis for hybrid circuits. The output gave the temperature distribution for each power-dissipating element hi the hybrid circuit. The program was based on Laplace's equations using Fourier techniques in order to facilitate the process. Bessel's inequality allows one to input the desired accuracy and to determine where the infinite series should be truncated. Theoretically, the program will attain any desired accuracy less than 100%, but practical considerations of computer run time limit accuracies to 90-98 %. Accurate knowledge of thermal distribution can aid in device layout and packaging for optimum power dissipation, especially for the compact recent modern microelectronic circuits. Two and three-dimensional representations, for some examples summarizing typical solutions, have been included to illustrate problem solving techniques. Both, heat dissipation in screen-printed resistors, and in mounted components such as transistors and integrated circuits were taken into account.