Phase change material (PCM)-based thermal management is one of the most promising approaches for the thermal management of energy conversion devices such as electric vehicle batteries and photovoltaic cells. However, most of the PCM present inherently low thermal conductivities, which result in deficient temperature control capacity in these applications. Several types of carbon-based nanoparticle have been explored to enhance the thermal conductivity of pure PCM. Despite the significant improvements in their thermal conductivity, the heat transfer in the liquid phase nano-enhanced PCM is expected to decrease due to the presence of the nano particles matrices. In this study, three types of carbon-based nanostructures are embedded in a paraffin to investigate their heat transfer performance for thermal management applications. The experimental results indicate that the addition of nanoadditives can improve the heat conduction of solid phase paraffin with slight latent heat degradation. But it also drastically increases the dynamic viscosity of composites which suppresses the natural convection heat transfer in the melted PCM. The thermal behavior of nanocomposites during the melting process is experimentally and numerically examined. Results reveal that adding carbon nanofibers and graphene platelets deteriorate the thermal performance of the pure paraffin. However, an enhanced thermal response observed when graphite-based nanocomposites at 7.5 and 10 wt% are used due to their 620% and 1100% solid phase thermal conductivity enhancement, respectively. The results of the current work suggest that there is a trade-off between the thermal conductivity enhancement and natural convection suppression of nanocomposites that can be used in the optimal design of PCM-based thermal management systems.