To improve the heat dissipation efficiency of batteries, the eutectic mass ratios of each component in the ternary low-melting phase change material (PCM), consisting of stearic acid (SA), palmitic acid (PA), and lauric acid (LA), was explored in this study. Subsequently, based on the principle of high thermal conductivity and low leakage, SA–PA–LA/expanded graphite (EG)/carbon fiber (CF) composite phase change material (CPCM) was prepared. A novel double-layer CPCM, with different melting points, was designed for the battery-temperature control test. Lastly, the thermal management performance of non-CPCM, single-layer CPCM, and double-layer CPCM was compared via multi-condition charge and discharge experiments. When the mass ratio of SA to PA is close to 8:2, better eutectic state is achieved, whereas the eutectic mass ratio of the components of SA–PA–LA in ternary PCM is 29.6:7.4:63. SA–PA–LA/EG/CF CPCM formed by physical adsorption has better mechanical properties, thermal stability, and faster heat storage and heat release rate than PCM. When the CF content in SA–PA–LA/EG/CF CPCM is 5%, and the mass ratio of SA–PA–LA to EG is 91:9, the resulting SA–PA–LA/EG/CF CPCM has lower leakage rate and better thermal conductivity. The temperature control effect of single-layer paraffin wax (PW)/EG/CF CPCM is evident when compared to the no-CPCM condition. However, the double-layer CPCM (PW/EG/CF and SA–PA–LA/EG/CF CPCM) can further reduce the temperature rise of the battery, effectively control the temperature and temperature difference, and primarily maintain the battery in a lower temperature range during usage. After adding an aluminum honeycomb to the double-layer CPCM, the double-layer CPCM exhibited better thermal conductivity and mechanical properties. Moreover, the structure showed better battery temperature control performance, while meeting the temperature control requirements during the charging and discharging cycles of the battery.