The sequence for adapting a conjugate mathematical model describing external heat exchange in the work space and heat exchange and hydrodynamics of the melt in a glass-melting furnace melting tank with horseshoe-shaped flame direction was examined. It was shown that it is sufficient to use the experimental dependences of the air heating temperature and temperature of the glass melt at the outlet of the melting tank on the furnace efficiency for adapting the model when the basic modeling boundary conditions have been correctly assigned. Equations were obtained that establish the correlation of the specific heat rate and maximum melting temperature and the specific output of glass melt, and they can be used in constructing an algorithm for controlling the thermal work of a glass-melting furnace of the design studied.