The structural and electro-thermophysical characteristics of organosilicon elastomers modified with multilayer carbon nanotubes (MWCNTs) synthesized on Co-Mo/Al2O3-MgO and metallic (Cu or Ni) microparticles have been studied. The structures were analyzed with scanning electron microscopy (SEM), transmission electron microscopy (TEM), Raman spectroscopy, and energy-dispersive X-ray spectroscopy (EDX). The main focus of this study was the influence of metallic dispersed fillers on the resistance of a modified elastomer with Cu and Ni to the degradation of electrophysical parameters under the action of applied electrical voltage. The distribution of the temperature field on the surface of a modified polymer composite with metallic micro-dimensional structures has been recorded. The collected data demonstrate the possibility of controlling the degradation caused by electrical voltage. It has been found that repeated on/off turns of the elastomer with an MWCNTs on 50 and 100 cycles leads to a deterioration in the properties of the conductive elastomer from the available power of 1.1 kW/m2 (−40 °C) and, as a consequence, a decrease in the power to 0.3 kW/m2 (−40 °C) after 100 on/off cycles. At the same time, the Ni additive allows increasing the power by 1.4 kW/m2 (−40 °C) and reducing the intensity of the degradation of the conductive structures (after 100 on/off cycles up to 1.2 kW/m2 (−40 °C). When Ni is replaced by Cu, the power of the modified composite in the heating mode increases to 1.6 kW/m2 (−40 °C) and, at the same time, the degradation of the conductive structures in the composite decreases in the mode of cyclic offensives (50 and 100 cycles) (1.5 kW/m2 (−40 °C)). It was found that the best result in terms of heat removal is typical for an elastomer sample with an MWCNTs and Cu (temperature reaches 93.9 °C), which indicates an intensification of the heat removal from the most overheated places of the composite structure. At the same time, the maximum temperature for the Ni additives reaches 86.7 °C. A sample without the addition of a micro-sized metal is characterized by the local unevenness of the temperature field distribution, which causes undesirable internal overheating and destruction of the current-conducting structures based on the MWCNTs. The maximum temperature at the same time reaches a value of 49.8 °C. The conducted studies of the distribution of the micro-sizes of Ni and Cu show that Cu, due to its larger particles, improves internal heat exchange and intensifies heat release to the surface of the heater sample, which improves the temperature regime of the MWCNTs and, accordingly, increases resistance to electrophysical degradation.