Alkanes and their mixtures (paraffins) have widely been used as phase change materials (PCMs) for low-to-medium temperature thermal energy storage. Among the various alkanes, eicosane, with a nominal melting temperature of 37 degrees C, has emerged in energy-storage-based passive thermal management technologies, for electronics for example. In an effort to increase the thermal conductivity of eicosane, the effect of adding graphene nanoplatelets (GNPs) as thermally conductive nanofillers was investigated experimentally. The composite PCM samples were prepared by dispersing GNPs in liquid eicosane at various loadings (0, 1, 2, 5, and 10 wt.%) without any surfactants. Thermal conductivity of the composite PCM samples in their solid phase was then measured by means of the transient plane source technique at elevated temperatures from 10 to 35 degrees C. Latent heat of fusion and melting point of the samples were also characterized using a differential scanning calorimeter. It was shown that for the highest loading examined (10 wt.%), the relative thermal conductivity enhancement is above 400% at 10 degrees C, indicating that the emerging GNPs have much better performance than the conventional nanofillers attempted in the available literature, such as metal/oxide nanoparticles and carbon nanotubes. Reduced thermal interface resistance, related to the unique two-dimensional planar morphology of GNPs, was interpreted to be responsible for their superior performance. The matrix/filler thermal interface resistance was estimated to range from 6 x 10(-9) to 9 x 10(-9) m(2) K/W. In contrast to the markedly increased thermal conductivity, however, the penalty of decrease in the energy storage capacity, caused by the presence of GNPs, was shown to be less significant.