The relevance of the subject of research is determined by the need to develop and subsequently implement a mathematical model and the corresponding structural scheme of the convective heating surfaces of the TP-92 steam boiler. The purpose of this research work is to directly model the heat- -transfer system of the convective heating surfaces of this boiler, designed for effective use in real conditions. The basis of the methodological approach in the research work is a combination of methods of the system analysis of the key principles of constructing mathematical models of heat-transfer systems of modern steam boilers with an experimental study of the prospects for creating a mathematical model of a heat-transfer system of the convective heating surfaces of a TP-92 steam boiler. In the course of the study, the results were obtained and presented in the form of a mathematical model of a convective heat-transfer system. It allows for making effective mathematical calculations of the main operating modes of the TP-92 steam boiler and calculating the dependences of the temperature and thermal modes of its operation on the change of incoming parameters of the used heat carriers, changes in the heating surface area and the relative flow rate of the heat carriers over the time of their use. The results obtained in the study, including the conclusions formulated on their basis, are of significant practical importance for the designers of steam boilers. The results also are useful for maintenance personnel, whose immediate responsibilities include determining the real possibilities of improving the convective heat-transfer system, based on the known parameters of the temperature of the coolant at the entrance to the system and at the exit from it.