In recent year, fatty acids (FAs) are heavily studied for heat storage applications and they have shown promising advantages over other organic phase change materials (PCMs). Among the FAs; capric, palmitic and stearic acids are the most studied PCMs. Several researchers have investigated these FAs and tried to improve their thermal properties, mainly by adding different high conducting fillers, such as graphite, metal foams, CNTs, graphene etc. In most cases, these fillers improved the thermal conductivity and heat transfer property but reduce the heat storage capacity considerably. These composites also lose the mixing uniformity during the charging and discharging process. To overcome these issues, selected FAs were grafted on the functionalized CNT surfaces and used as conductive fillers to prepare FA based composite PCMs. This process significantly contributed to prevent the drastic reduction of the overall heat storage capacity and also showed better dispersion in both solid and liquid state. Thermal cycling test showed the variations in the thermal energy storage values of all composite PCMs, however, within the tolerable grade and they had appreciable phase change stability and good chemical stability even after 2,000 cycles.