Effective cooling mechanisms are crucial for electronic apparatus to improve dependability and prevent premature failures. This study investigates the impact of pin–fin heat sink design on heat transfer performance in electronic apparatus cooling, employing Phase Change Materials (PCMs). Two-dimensional transient simulations are conducted by varying the thickness of pin fins in heat sinks, while maintaining the pin fin length and the volume fraction of Thermal Conductivity Enhancer (TCE) constant. Heat sinks equipped with fins of thickness 1 mm, 2 mm, and 3 mm are utilized while maintaining a consistent fin volume fraction of 9%. The PCMs utilized include N-eicosane, Paraffin, RT 54, and RT 42. Finite-volume method and conjugate heat transfer equations model the heat transfer between solid and fluid regions. Results indicate that lower melting point PCMs maintain lower base temperatures for shorter durations, while higher melting point PCMs sustain operating limits for longer periods. A 2 mm fin thickness proves optimal, offering superior heat transfer performance and extended PCM melting times. Paraffin offers higher melting time, thus improving the temperature-controlling capability of the passive cooling system when compared to the cases with n-eicosane, RT 54, and RT 42.