A power surge is a frequent phenomenon that occurs in electronics. Inadequate and improper cooling during power surges results in a rapid increase in operating temperatures that may lead to failure of the electronics. In the present investigation, the thermal characteristics of a phase change material (PCM)-based heat sinks, having different configurations and orientations of fins, subject to (i) constant heat load and (ii) heat load with a power surge, are studied numerically. Preliminary investigations showed that a heat sink with PCM gets heated at a much lower temperature than an air cooled heat sink. Following this, four finned heat sinks are considered for further investigations. The heat sink with PCM, sans fins, is used for baseline comparison. The orientation of fins in the other four heat sinks is either vertical or horizontal with square and rectangular cross sections. The heat sink and fins are made of aluminum, and the PCM used is n-eicosane (C20 H42). The enthalpy-porosity method is used to model the solid–liquid phase change in the PCM. All the transient three-dimensional numerical simulations are carried out using ansys fluent 15.0. For a constant heat load of 5 W and power surges of various magnitudes at different time instants, the heat sink with vertical square fins shows superior performance. However, the performance variation among the heat sinks with different fin configurations is insignificant for constant heat load. Even so, for power surges, the location and the configuration of fins have a significant effect on the heater temperature. Cases with high power surge and shorter duration of the surge were also considered to critically examine the effect of fins in controlling the maximum temperature in the heat sink. The numerical results of the best-performing heat sink, i.e., the heat sink with vertical square fins, are finally validated against in-house experiments.