This study aims at investigating the effect of nanoparticle morphology and concentration on the specific heat capacity of a molten salt used as thermal energy storage material in concentrated solar power plants. Binary carbonate salt eutectic (lithium carbonate and potassium carbonate at a molar ratio of 62:38, respectively) is used as the base material. Two different carbon allotropes, graphite nanoparticles (Gp) and carbon nanotube (CNT) are used as dopants to look into the morphological effect on specific heat (Cp). A series of experiments are carried out to systematically investigate the effect of nanoparticle concentration by varying the mass percentages of carbon allotropes (2 wt.%, 4 wt.%, and 6 wt.%) in the base material. The specific heat capacity of the samples is measured both in solid (250 °C and 400 °C) and liquid phases (520°–560 °C) using a differential scanning calorimeter (DSC). The results show a maximum enhancement of 35% in Cp for 6 wt.% Gp -based salt in the liquid phase. CNT-based nanomaterials exhibit a maximum enhancement of 20% for 4 wt.% CNT inclusion in the liquid phase. The superior performance of Gp compared to CNT and mass concentration-controlled specific heat is explained using field emission scanning electron microscope (FESEM) and energy-dispersive X-ray spectroscopy (EDS) analysis. FESEM and EDS analysis confirm the presence and the composition of the compressed layer, respectively. These layers are considered to be responsible for the anomalous increase in specific heat capacity at different mass concentrations for the carbon allotropes.