The linear and nonlinear mathematical models for determining the temperature field and subsequently analyzing temperature regimes in isotropic spatial media subjected to external local thermal load are developed. In the case of a nonlinear boundary value problem, the Kirchhoff transform is applied to linearize the nonlinear heat conduction equation and nonlinear boundary conditions, resulting in a linearized second-order partial differential equation with a discontinuous right-hand side and partially linearized boundary conditions. For the final linearization of the partially linearized boundary conditions, the temperature was approximated by the spatial coordinate on the boundary surface of the heat-sensitive medium by a piecewise constant function, which made it possible to obtain a linear boundary value problem with respect to the Kirchhoff transform. The method of the integral Fourier transform was used to solve the linear boundary value problem and the resulting linearized boundary value problem, which resulted in the analytical solutions of these problems. For a thermosensitive medium, as an example, the linear dependence of the thermal conductivity of the structural material of a structure on temperature, which is often used in many practical problems, is chosen. As a result, an analytical solution in the form of a non-proprietary integral is obtained to determine the temperature distribution in this medium. A numerical analysis of the temperature behavior as a function of spatial coordinates for given values of geometric and thermophysical parameters is performed. To determine the numerical values of the temperature in the above structure, as well as to analyze the heat transfer processes caused by locally concentrated heat flux, software tools have been developed that have been used to perform a geometric representation of the temperature distribution depending on the spatial coordinates. The developed linear and nonlinear mathematical models for determining the temperature field in spatial environments with external heating show that they are adequate to the real physical process. They make it possible to analyze such environments in terms of their thermal stability. As a result, it becomes possible to increase it and protect against overheating, which can cause failure not only of individual components and their individual elements, but also of the entire structure.
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