Understanding the shaped-charge jet-initiation mechanism of covered explosives and the effect of explosive temperature is important for ammunition safety. We devised a method of using a shaped-charge jet-penetrating cover to shock-initiate heated explosives. This method achieves uniform temperature control of explosives via heating the upper and lower ends and preserves heat on the side of the explosive charge. We experimentally tested the method on hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX)-based aluminized explosives (61 wt.% RDX, 30 wt.% Al, 9 wt.% binder) at different temperatures and cover thicknesses. The jet-penetration behavior and explosive detonation-wave growth were observed via X-ray photography, and the effect of explosive temperature on jet initiation was analyzed. A numerical model of the shaped-charge jet-initiating explosive was set up by considering the temperature change of the explosive and analyzing the detonation-wave growth and initiation thresholds of different explosive temperatures under jet shock initiation. Under a thin cover, the explosive showed prompt impact initiation by the jet; the initiation occurred very near to the explosive surface. However, for a thick cover, the explosion was initiated by a bow wave formed at a certain distance from the upper surface of the explosive, and a retonation wave was observed. The temperature of RDX-based aluminized explosives affects the two jet-initiation mechanisms. The shock sensitivity of the explosives to the jet decreased with increasing temperature, but the shock sensitivity increased when the temperature exceeded a certain value. A simulation method was established that can be used to predict shaped-charge jet initiation at different explosive temperatures. We obtained the relationship between the cover thickness and run-to-detonation distance under jet shock initiation, which provides a theoretical basis for safety analysis and evaluation of a warhead charge that is attacked by a shaped-charge jet.