Both storage and transport of medical products remains a challenging task because of many variables as well as infrastructures, territory, and so on. Among these variables, monitoring the medical products temperature is fundamental to guarantee their safety. On the other hand, for sectors like aerospace delivery, weight has a crucial role too. For such applications and especially for strongly variable external temperatures, Peltier cells might be employed for either cooling or heating medical products to be stored. Accordingly, this study addresses the optimization of a heat sink for the thermal management of a Peltier-cell-based biomedical refrigerator. In detail, a brute-force multi-objective optimization of an impinging-flow finned heat sink for the Peltier cell is carried out here. Thermal resistance, weight, and pressure drop are chosen as the three-objective functions to be minimized, with both geometrical and volumetric flow rate as design variables. The results present a very large bunch of optimal solutions to design such devices. With the utopia optimum criterion, Rth = 0.159 °C/W, msink = 0.550 kg, and Δp = 14.99 Pa are obtained. Finally, both multiple-linear regression and artificial neural networks are employed to relate design variables with the objective functions, in order to provide the final user with a practical tool for the optimal design of such devices.