The article shows the results of mathematical simulation of convective turbulent heat transfer in the closed domain with heat-conducting walls and the source of heat emission. The system of equations in the model of thermal conductivity for the solid walls and Navier-Stokes equations for gas are solved. The article examines the possible versions of the calculation of the turbulent regime in the geometrically simple air region by means of conducting the simulation within the framework of algebraic models (Van Driest and Prandtl-Reichardt), and k-ε model. On the basis of the obtained results the authors made a conclusion about the possibility of applying the algebraic model of Prandtl to describe the integral characteristics of turbulent flows in the conditions of natural convection in a geometrically simple area when the air heated by the heat source is moved by the lifting force. Besides, the temperature fields for a typical real object of heat supply are simulated in the article. The values of the dimensionless heat exchange coefficient at the air-wall interface are determined. The comparative analysis of two quite significantly different approaches to determine the average temperature in the heated room, i. e. the traditional balance approach and the approach based on the considered system of partial differential equations is executed. It is concluded that the balance models of the calculation of the temperature regime can adequately describe real temperatures of heat supply objects only for very large values of the characteristic times of the processes in question.