Phase-change cold storage technology is recommended as a solution for energy conservation and carbon neutrality in air conditioning systems of buildings. This study focuses on the development of binary composite phase-change materials comprising octanoic acid–tetradecanol (OA-TD). To enhance its thermal conductivity, expanded graphite (EG) was employed as an additive carrier, and the surface modification of EG particles using hexadecyltrimethoxysilane (HDTMOS) was attempted to make up for the instability and further to improve the performance of OA-TD/EG CPCMs. The OA-TD/EG-HDTMOS CPCMs were synthesized by EG mixed with EG-HDTMOS at a 1:1 mass ratio. The thermal performance and stability of the OA-TD/EG-HDTMOS CPCMs were thoroughly evaluated by multi-cycle melting–solidification and thermal conductivity measurements. The results revealed that the OA-TD mixture, when at a mass ratio of 77:23, exhibited a phase-transition temperature of 11.4 °C and a latent heat ranging from 150 to 155 J/g. Then, the OA-TD/EG-HDTMOS composite material, at a 12:1 mass ratio of OA-TD to EG-HDTMOS, solidified and melted at temperatures of 9.2 °C and 11.2 °C, with a latent heat ranging from 138 to 143 J/g, and significantly improved the thermal conductivity to 0.7 W/(m·K), representing a remarkable 133% increase compared to that of OA-TD alone. Even after undergoing 100 melting–solidification cycles, the OA-TD/EG-HDTMOS maintained superior phase-change thermal performance and stability, making it suitable for cold storage and energy conservation in air conditioning.