This study focused on developing an efficient phase change material (PCM) with a stable shape that can be applied in a wide range of industries. To prevent leakage of the PCM liquid at a temperature above the melting point, we used an encapsulation method by making use of an interfacial polycondensation reaction, and attempted to develop a new PCM with excellent thermal conductivity and thermal energy storage capacity. In order to improve the functionality of the PCM in latent thermal storage applications, a magnetic material, Fe3O4, was mixed with n-eicosane and a shape-stable phase change microcapsule with a silica shell was successfully prepared. In this study, we loaded Cu metal nanoparticles on the outer wall of the capsule with the aim of improving the thermal conductivity of the material for efficient heat transfer. The results indicated that the n-eicosane-Fe3O4@SiO2@Cu microcapsule has excellent heat transfer ability owing to its high thermal conductivity and exhibits efficient thermal energy storage–release performance by suppressing supercooling. The n-eicosane-Fe3O4@SiO2@Cu microcapsule showed an encapsulation efficiency (Een) of 61.48%, an energy storage efficiency (Ees) of 61.47%, and a thermal storage capacity (Ces) of 99.99%. Moreover, the multi-cycle differential scanning calorimetry scan showed excellent thermal reliability and shape stability, even in repetitive melting–cooling processes, suggesting that it is a promising PCM that can be used in industrial applications.