The phase change material (PCM)-based battery thermal management technology still remains a contradiction of guaranteeing a suitable operating temperature (20-40 degrees C) of the batteries under regular working conditions, while avoiding the malfunction of the PCM under high ambient temperature (>40 degrees C). Therefore, a novel composite PCM (CPCM) possessing dual phase change temperature regions (PCTRs) is designed herein by in-situ constructing a phase-changeable polymer (PCP) framework in the polyethylene glycol (PEG)/expanded graphite (EG) slurry. As prepared, the lower PCTR at 31.7-42.1 degrees C from the PCP framework provides a latent heat of 35.0 J g-1, while the higher PCTR at 42.1-51.2 degrees C from the PEG offers a latent heat of 68.3 J g-1. Additionally, the nanoscaled PCP framework strongly adsorbs the PEG, preventing the leakage phenomenon (mass loss < 1%), and the uniformly dispersed EG endows the CPCM with a high thermal conductivity of 1.98 W m-1 K-1. In consequence, under the normal ambient temperature of 25 degrees C, the lower PCTR effectively keeps the battery module operating within the suitable temperature range of 25.9-34.9 degrees C and with a low temperature difference (Delta T) of 2.4 degrees C at the discharge rate of 1C. For comparison, the battery module adopting classical CPCM with a single PCTR at 40.9-55.1 degrees C demonstrates a much higher temperature range and maximum Delta T at 28.0-40.9 degrees C and 4.8 degrees C, respectively. Under the high ambient temperature of 40 degrees C, the higher PCTR starts to work like the single PCTR of traditional CPCMs, and controls the Tmax and Delta T of the module below 49.2 and 2.2 degrees C at the discharge rate of 1C, respectively, preventing thermal hazards.