This article examines the issues of developing mathematical models for optimizing the parameters of the thermal action on the technical systems. The authors set the task of determining the optimal parameters of sources of temperature field disturbance in the technical system under the appropriate restrictions. Considering the technical characteristics of the means that ensure the process of thermal action on the material, and the peculiarities of the technological process, appropriate restrictions on the temperature field and its components are set. Checking the limits of the temperature field requires multiple calculations, which reduce thermal damage to parts of the material. To automate the objective function, it is possible to use grid processors, which, due to the use of specialized functional blocks, solve a huge number of boundary problems with computers almost instantly. Because to the selection of solutions of boundary value problems, this will allow to find optimal values of technical parameters, and therefore to increase the accuracy of the simulated process. The research of this article refers to the section on mathematical modeling and optimization of systems with distributed parameters. For mathematical modeling of these systems, boundary value problems of differential equations with partial derivatives are used. The authors present applied optimization mathematical models for controlling the distribution of the temperature field and thermal stresses in the material, minimizing its damaged parts. The last them is based on the differential criterion for evaluating the temperature of irradiation and can be used to optimize many technical, biotechnological and economic systems. A detailed analysis of the specific features of applied optimization mathematical models will allow to increase the accuracy of the development of numerical methods and hardware and software tools for calculating and optimizing the parameters of simulated systems.