This paper provides an analysis of the benefits of passive cooling for High Concentrator Photovoltaic (HCPV) systems in terms of costs and kWh annual energy yields. For the first time, the performance of the heat sinks has been related to the calculated energy yield of a standard triple-junction GaInP/GaAs/Ge HCPV cell in a system deployed at several suitable locations across the globe. Copper and aluminium heat sinks have been considered and their merits have been compared. The finite element analysis software package COMSOL was employed to gain insights regarding a simple flat plate heat sink. The cell temperature was found to have a linear dependence on the geometric concentration with a characteristic slope that increases with cell size (ranging from 10 to 0.25mm). The results show the advantages of miniaturisation, and that the cooling of smaller cells can be accomplished using flat heat sinks. Within the considered range of geometric concentration ratios (up to 1000×), aluminium heat sinks are, in general, found to be preferred over copper, because of their lower densities and costs for the same thermal management. Closed-form thermal models based on the Least-Material (LM) approach have been utilised to design more complex finned heat sinks (operated under natural convection) that yield the best compromise between thermal performance and weight. For a 60°C cell operating temperature, a greater kWh output is obtained, but an LM heat sink designed for a cell temperature of 80°C has a material cost per unit energy that is between 50% and 70% less than the one designed for 60°C. Heat sink costs between $0.1 and 0.9 per Wp were estimated for a geometric concentration above 500suns, depending on the cell׳s temperature and size. There are strong reductions in HCPV installation costs by limiting the dimensions of the cooling system at high concentrations