The effects of carbon nanotube fillers on the transient performance of thermal energy storage-based heat sinks for electronics were experimentally analyzed in order to assess the potential of nanocomposite phase change materials as applied to thermal energy storage-based thermal management technologies. 1-hexadocanol and multi-walled carbon nanotubes were chosen as the matrix phase change material and fillers, respectively, to form nanocomposite phase change materials at various mass fractions (0.3%, 1%, and 3%), whose key thermophysical properties were characterized. Under the intensive pulsed heat loads (up to 7.0 W/cm2), the transient performances of the heat sinks (finned or unfinned) were compared with respect to the mass fraction of carbon nanotubes in the nanocomposite phase change materials. Results show that the performance of the heat sink is slightly deteriorated upon adding carbon nanotubes into 1-hexadocanol as a result of greatly suppressed natural convection effects during melting, due to the dramatically increased viscosity. Then the performance improvement caused by enhanced heat conduction was offset, even if the thermal conductivity of the nanocomposite phase change materials was increased by the addition of carbon nanotubes.