The advisability of constructing a CAD system for glass-melting furnaces is demonstrated. The main principles of the mathematical support for the CAD technological subsystem are formulated. The principles of constructing a mathematical model of the thermal performance of a furnace are described. The main equations providing for a combined solution of the exterior and the interior problems of heat and mass exchange taking into account the specifics of the physiochemical aspects of the glass-melting process are given.