Designing an effective heat sink that is light, inexpensive, and simple to manufacture and install, is crucial in developing a heat control strategy for high concentrated triple-junction (TJ) solar cells to maintain the cell operating temperature below the maximum allowed limit. Such heat sinks ensure better electrical output power and efficiency at a cheaper cost. Thus, the present research focuses on the passive thermal regulation of a triple-junction solar cell utilizing four different finned heat sink configurations; (A) flat plate, (B) straight fins, (C) pin fins, and (D) flared fins heat sink. A comprehensive 3D thermal and electrical model is developed and computationally simulated, incorporating the cell module layers coupled with the aluminium heat sink. The performance of the proposed system with different heat sink designs is investigated at various concentration ratios (CR) of the solar irradiance ranging from 50 suns to 1250 suns, air temperatures ranging from 25 °C to 40 °C, and wind speeds ranging from 1 m/s to 5 m/s. In hot climatic conditions (40 °C and 1 m/s), the integration of the proposed heat sink configurations A, B, C, and D enables the cell to operate safely (below 110 °C) at high concentration ratios of 440 suns, 1435 suns, 1250 suns, and 1775 suns, respectively, and produce large electric power of 15.2 W/cm2, 49.7 W/cm2, 43.3 W/cm2, and 61.4 W/cm2. In contrast, the maximum permissible concentration ratio of an uncooled cell operating in the same conditions is limited to 77 suns with an electrical output of 2.7 W/cm2. Although the flared fins heat sink is the heaviest, weighing about 0.6 kg, and the flat plate one is the lightest with 0.05 kg, the environmental analysis revealed that utilizing the former for cooling concentrated photovoltaic systems could reduce annual CO2 emissions by 1475.2 tons/m2 compared to 364.5 tons/m2 for the latter if both are operated at the maximum permissible solar concentration ratio.