During the study and control of temperature distributions in moving and stationary axisymmetric elements of complex systems, mathematical models of heating processes play an important role. Unlike natural measurements of temperature in a finite number of points, these models help to analyze the temperature field in the entire heating area. The goal of this paper is to build a mathematical model of temperature distributions in moving and stationary axisymmetric elements of complex systems in the form of a nonlocal problem for the heat conduction equation with an integral condition, to develop a method for solving the nonlocal inverse problem. For the practical use and application of the mathematical model in the design of technological equipment, it is important to determine the control parameters of the temperature distribution. By introducing an integral condition to the mathematical model of the thermal process that occurs in a moving axisymmetric area, the control parameters of the temperature field are determined. In the paper, as additional information for formulating the inverse problem, a nonlocal integral condition is used, which is constructed based on the thermal energy balance condition in the heating area. This made it possible to increase the efficiency of temperature control in complex systems. A method for solving the nonlocal inverse problem of thermal conductivity was proposed.