Through the example of the U-flame glass-melting furnace with a productivity rate of 280 tons per day it was investigated in the article how the structure of the heat exchanger's brickwork influences the checker-work's volume providing the air heating up to 1300 °C. The brickwork structure for the single-turn heat exchanger was designed which has the heat loss factor 0,979 and the inward leakage factor 0,1. Both the energy efficiency and gas tightness of the heater exchanger's brickwork are provided by the multilayer structure in which the modern heat insulating materials are used. The newly developed brickwork structure reduces twofold the external heat losses comparing to the knows technical solutions. The heat flows through the heat exchanger's roof and walls are 961,9 and 183,1‒820,4 kW/m2 respectively.