The mass content of expanded graphite (EG) in fatty acid/expanded graphite composite phase-change materials (CPCMs) affects their thermal properties. In this study, a series of capric–myristic acid/expanded graphite CPCMs with different EG mass content (1%, 3%, 5%, 8%, 12%, 16%, and 20%) were prepared. The adsorption performance effect of EG on the PCMs was observed and analyzed. The structure and thermal properties of the prepared CPCMs were characterized via scanning electron microscopy, differential scanning calorimetry, thermal conductivity measurements, and heat energy storage/release experiments. The results show that the minimum mass content of EG in the CPCMs is 7.6%. The phase-change temperature of the CPCMs is close to that of the PCMs, at around 19 °C. The latent heat of phase change is equivalent to that of the PCM at the corresponding mass content, and that of phase change with an EG mass content of 8% is 138.0 J/g. The CPCMs exhibit a large increase in thermal conductivity and a significant decrease in storage/release time as the expanded graphite mass content increases. The thermal conductivity of the CPCM with a mass content of 20% is 418.5% higher than that with a mass content of 5%. With an increase in the EG mass content in CPCMs, the heat transfer mainly transitions from phase-change heat transfer to thermal conductivity.