The residual stress of metal liners wrapped by composite materials has a significant influence on the service performance of rotating parts, such as flywheel rotors and motor jackets. However, the deformation of the liners, the flow of resins, and the temperature variation during the winding process make it difficult to predict and control this residual stress. In this paper, the process-induced strains were monitored online by a strain gauge with the help of a wireless strain meter. The evolution of this strain during the manufacturing process was fully discussed. A rapid curing resin system was used and its curing properties were tested by differential scanning calorimetry. The mechanical properties of the resin matrix and its composite were characterized. The effect of the curing cycle on the evolution of the residual strain was discussed in detail through comparative experiments. The experimental results show that the use of infrared radiation has a significant advantage regarding residual stress accumulation. This advantage is greater when carbon fiber is used than when glass fiber is used. The prestress in composites of glass fiber and carbon fiber increases by 5.9% and 41.7%, respectively, after cooling.