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An electrical insulation made as a hollow circular cylinder with unlimited length is considered under a constant difference of electric potentials on cylindrical surfaces. The cylinder material is a composite with a polymer matrix modified by heat-conducting dispersed granules improving characteristics of the electrical insulation. The nonlinear mathematical model of the temperature state of the electrical insulation is constructed for given density of the heat flow on the inner surface of the cylinder and the heat exchange conditions specified on its outer surface. Results of the quantitative analysis of this model allow us to determine the maximal potential difference just before the thermal explosion of the electrical insulation and to find out possible applications of polymer composites with heat-conducting dispersed inclusions as dielectrics in various high-voltage electrical and electro-physical devices, among others, as electrical insulation of conducting strands of high-voltage DC cables.