Polymer dielectrics capable of operating at elevated temperatures are essential components in advanced electronics and electrical power systems. However, dielectric polymers generally display significantly deteriorated capacitive performance at high temperatures because of exponential growth of electrical conduction. Here we design and prepare the cross-linked copolymers with interrupted translational symmetry and the use of local disorder-induced electron localization (i.e., Anderson localization) to impede electrical conduction of the copolymers. Consequently, the copolymer exhibits state-of-the-art discharged energy density of 3.5 J cm−3 with a charge–discharge efficiency of 90% at 250 °C. The copolymer also displays much more stable capacitive energy storage performance in the temperature range of 25 to 250 °C compared to existing dielectric polymers. With the demonstrated breakdown self-healing ability and excellent cyclability of the copolymer, this work sheds a new light on the design of high-temperature high-energy-density polymer dielectrics.