The present study introduces a novel fin–Phase Change Material (PCM)–Expanded Graphite (EG) composite for better thermal management of a Panasonic NCR18650BD battery at discharge rates higher than its maximum discharge limit 2C. Fins and EG are augmented with PCM to enhance its effective thermal conductivity. Initially, the electrical and thermal behaviors of the battery are simulated for 0.5, 1, and 2C discharge rates using the Newman P2D model, and these are validated against in-house experiments. Following this, the heat generation profiles are estimated from the numerical model to mimic the battery with a heater in the experiments conducted to propose an effective thermal management system for 2, 3, and 4C discharge rates. Three heat sinks, one sans fins, and the other two with 130 and 260 fins, respectively, are considered to perform experiments. Phase Change Material (PCM) named Eicosane (Ei) with an addition of 0, 10, 20, 25, and 30% weight fractions of EG is filled in the heat sinks to study the effect of composite PCM on the thermal regulation of the battery. The heat sink having 260 fins filled with 70% Ei - 30% EG composite outperforms the other heat sinks considered in this study by recording lower temperatures to the extent of 17.5, 20.5, and 22.7 °C than a plain heat sink filled with 100% Eicosane for discharge rates 2, 3, and 4C, respectively. Furthermore, with the addition of 30% EG by volume, the maximum thermal performance of heat sink having 130 fins surpasses the heat sink having 260 fins filled with pure Eicosane by recording 1.3, 0.5, and 1.5 °C lower temperatures for discharge rates 2, 3, and 4C, respectively. In view of this, a possible engineering solution is to employ a simple heat sink, having fewer fins filled with PCM–EG composite instead of intricate heat sinks, having more fins filled only with the baseline PCM, to overcome the design difficulties and manufacturing costs.