The mathematical model of the complex heat exchange in the flame space of the tank furnace glass melting zone in developed. The calculations of the temperature fields in gas space and at the inner crown surface, the fields of heat absorption density, the consumption part of the heat balance of the furnace make it possible to use this model successfully for the detailed analysis and forecasting of the furnace heat operation. The model can be used for the practical realization of the automated control system based on the microprocessor technics.