Since the pioneering introduction of the microchannel heat sink by Tuckerman and Pease [1], many investigators have studied heat transfer phenomena within these heat sinks. Their efforts have been aimed at presenting an optimized structure for the microchannel heat sink. This paper presents three optimization methods by which the thermal resistance of the microchannel heat sink can be minimized: the fin model, the porous medium model, and the numerical optimization method. Assumptions used in the fin model are shown to be invalid for large values of the aspect ratio, while the porous medium model is shown to accurately predict the thermal performance of the microchannel heat sink. Because of this defect, the fin model fails to provide the design variables. In addition, the optimized design variables and the corresponding thermal resistances are presented using the optimization methods based on the porous medium model and the numerical simulation under the constraint of a maximum pumping power.