This article reports on the development of nano-MgO/epoxy resin composites with various mass ratios via a solution blending method. The influence of MgO nanofillers on the thermal properties and the effect of environmental temperature on the insulating properties of the composite material were analyzed. The results show that the thermal conductivity of the composites increased with an increasing MgO nanofiller content. Compared with the pure epoxy resin, the thermal conductivity increased by 75% when the content of MgO nanoparticles was 7%. The volume resistivity first increased and then decreased with an increasing doping concentration. The volume resistivity increased by 26.8% in comparison with the pure epoxy resin when the content of MgO nanoparticles was 1%, while its dielectric constant and dielectric loss increased with temperature. In addition, the dielectric constant increased and the dielectric loss first decreased and then increased with an increasing MgO nanoparticle content. Moreover, the MgO composites changed from a glassy to a rubbery state, and the breakdown strength was significantly reduced with an increased temperature. When the temperature was higher than the glass transition temperature, the breakdown strength decreased by 51.3% compared with the maximum breakdown strength at 20 °C. As the content of MgO nanoparticles increased, the breakdown strength of the composite first increased and then decreased. The highest breakdown strength was achieved when the content of MgO nanoparticles was 1%, which was 11.1% higher than that of the pure epoxy resin. It was concluded that the MgO nanofillers can significantly improve the thermal properties of epoxy composites and their insulation performance at high temperatures.