The effect of exfoliated graphite (ExG) with myristic acid phase change material has been investigated to understand the enhancement of thermal conductivity and shape stabilization for the ExG-myristic acid composite system. The thermochemically synthesized ExG is added to myristic acid in 5, 10, and 15 wt\% and the shape stabilized ExG-myristic acid composite samples are prepared. The heat release, solidification time and latent heat of myristic acid and ExG-myristic acid composites are measured using temperature history (T-history) and Differential Scanning Calorimetric (DSC) measurements, respectively. The measured melting temperature and latent heat of fusion of myristic acid are similar to 55 degrees C and similar to 185 kJ/kg, respectively. Latent heat of ExG-myristic acid composite samples has decreased linearly with increasing ExG weight fraction. T-history measurements suggest the reduction in solidification time for ExG-myristic acid composite samples and similar to 55\% reduction in heat release time is observed for 15\% ExG-myristic acid composite sample with respect to pristine myristic acid. The observed reduction in heat release time subtantiates the effective enhancement of thermal conductivity for ExG-myristic acid composite samples.