The article is devoted to the investigation of thermal fluctuation processes in insulating materials in accordance with the theory of thermal conductivity for solving problems of diagnostics and forecasting the residual life of insulating materials on the basis of a non-destructive temperature method. Mathematical models are proposed that describe the layer-by-layer temperature distribution of the cable line in accordance with the theory of thermal conductivity using the differential Fourier equation. The analytical dependence of the determination of the temperature of the most heated insulation point (cable core) is refined, its transformation is performed to calculate the cable core temperature taking into account the temperature of the cable surface, the environment, and the vein current for various operating parameters of the power cable line (PCL). The software «System» for measuring and calculating the thermal fluctuation characteristics of SCR (SMaCTC), based on the mathematical model of the temperature field in the cable cross-section, has been developed. The software differs from the existing capability of layer-by-layer control of thermal fluctuation processes based on the temperature value on the cable surface. A comparative analysis of the experimental and calculated characteristics of the temperature distributions has been carried out, and various load modes of operation and functions of changing the cable current have been investigated.