At the design stage of power cable lines (PCL), according to the methodology in IEC 60287, its throughput is determined, taking into account all possible factors arising from the exploitation-select the coefficients that provide the reserve for heating, so in some cases the cables are under loaded, and sometimes operate at the limit of thermal stability. Currently, the technology of measuring cable distributed temperature is actively introduced, aimed at solving these problems and allowing to control the surface temperature of the cable in real time over the entire length of the PCL. Low thermal conductivity of cable insulation leads to a high temperature gradient, so the temperature of the most heated section in the cable section (near the core) is significantly different from the measured temperature, and in transient modes this difference can increase several times. Therefore, the problem of creating mathematical models and algorithms for estimating the transmission capacity, calculation and prediction of the PCL core temperature in real time on the basis of the data of the temperature monitoring system, taking into account the change in the current load of the line and the external conditions of the heat sink, is urgent.