To reduce car body weight, multi-material structures with lightweight materials such as carbon-fiber-reinforced plastics (CFRPs) and aluminum alloys (Als) are used to replace parts of steel components, and joining technologies for such dissimilar materials are essential. Friction stir spot welding (FSSW) is one of the technologies used to rapidly and strongly join dissimilar materials. FSSW for carbon-fiber-reinforced thermosetting resin (CFRTS) and Als has been developed using composite laminates with integrally molded thermoplastic resin in the outermost layer. To suppress excessive heating under the tool, this study investigated whether multi-stage heating with a non-heating time during joining affects the heat distribution and strength properties of the joint. Due to heat diffusion in Al during the non-heating time, multi-stage heating can suppress excessive heating under the tool compared to continuous heating, resulting in up to 27% larger welded area, up to 37% smaller decomposed area, and up to 6% lower maximum temperature. The use of multi-stage heating results in up to 5% higher tensile shear strength and 210% longer fatigue life by reducing the thermal decomposition of CFRP matrix resin and PA12 resin.