The methodology of theoretical studies of heat exchange processes in boiler units based on the mathematical model of burning coal dust has been developed. For the first time, the continuous curve of the fractional composition of an ensemble of coal particles is presented. The mathematical model is consistent with the aeromechanical and thermal characteristics of the torch, obtained on the basis of calculated and experimental data. The concept of a torch continuum is introduced as a continuous medium in which the processes of combustion and heat exchange are investigated. The methods of dividing the combustion chamber into zones, the equations of stationary and non-stationary heat conduction, radiation and convective heat exchange are used. These methods have been tested on a number of high-temperature installations, including boilers with natural circulation, for example, E-220 at the CHP plant in Bishkek, Kyrgyz Republic in the Central Asian region. In the course of the experiments, coals with different thermal characteristics were burned. In a special computer program obtained a 3D image of burning coal dust. Analysis of the calculated and experimental data showed a discrepancy between them of 4-5%. Analysis of computer simulation data showed a discrepancy with the calculated data of 3-4%, and with experimental 5-6%. Thus, the dependence of the parameters of the heterogeneous flame on the mathematical description of the fractional composition of coal dust is substantiated and the characteristics of the combustion process, previously not taken into account in the theory of heat transfer, are revealed. The task was solved-theoretically confirmed new methodological approaches to the theory of heat transfer in the furnace of the boiler unit.