Heat sink devices that use a phase change material (PCM) as a heat sink material, and methods of using such devices in thermal management applications. Such a heat sink device includes a base wall, a top wall spaced apart from the base wall, and an internal structure in intimate thermal and physical contact with the base wall and the top wall. The internal structure includes multiple compartments defined and separated by fins that extend between the base and top walls. At least one PCM is within the compartments and the fins serve as thermal enhancement structures to augment the surface area to volume ratio of the heat sink device.