In this study, thermal performance of a vertical plate-fin heat sink under natural convection was optimized for the case in which the fin thickness varied in the direction normal to the fluid flow. For this optimization, the averaging approach presented in an earlier paper for the case of the heat sinks under forced convection was extended to study the performance of heat sinks under natural convection. In the case of an air-cooled heat sink, the thermal resistance decreases by up to 10% when the fin thickness is allowed to increase in the direction normal to the fluid flow. However, the difference between the thermal resistances of heat sinks with uniform thickness and the heat sinks with variable thickness decreases as the height decreases and as the heat flux decreases. (C) 2011 Elsevier Ltd. All rights reserved.