Transparent heaters, which are capable of withstanding a high dynamic strain, in contrast with those made of brittle indium tin oxide films, are increasingly needed for heating of next-generation flexible and stretchable electronics, such as artificial skins, touch screens, displays, and sensors. This work provides a new approach for the fabrication of a transparent heater that is made of a Cu wire/alumina/polyimide composite film. The advantages of this film include a high transparency, low operating voltage, unprecedented stability against harsh environmental conditions, and repeated bending or stretching. A highly conductive Cu wire network was prepared via thermal evaporation of low-cost Cu on electrospun polymer nanofibers. Atomic layer deposition was used to conformably deposit an alumina film on the Cu wire network to suppress the diffusion and oxidation of Cu. The solution casted polyimide film that was introduced acts as a binder and can successfully improve the adhesion strength between the Cu wire and its substrate. After delicate optimization of the layered structure, we fabricated a transparent heater that exhibits a low sheet resistance of 8 Ω sq⁻¹ and a high visible light transmittance of up to 91.4%, and it demonstrated an unprecedented ability to resist temperatures as high as 300 °C. Furthermore, the Cu wire/alumina/polyimide-based transparent heater can endure 100 cycles of stretching–releasing at a strain of 30% with an exceptionally high stability and reversibility. Thus, these copper wire/alumina/polyimide composite films have extremely high potential for applications in heating of future wearable optoelectronic devices.