Paraffin is a stable organic phase change material (PCM); however, its broad application is constrained by its inherently low thermal conductivity. Incorporation high thermal conductivity nano-additives has proven to be an effective strategy for enhancing the thermal performances of paraffin. In this study, the thermal properties of pure octadecane paraffin, octadecane/copper oxide (CuO), and octadecane/carbon nanotube (CNT) composite PCMs are investigated using molecular dynamics simulations. Furthermore, the mechanisms underlying the thermal conductivity enhancements achieved with these nano-additives are explored. The results indicate that both CuO and CNT nano-additives substantially increase the thermal conductivity across a range of temperatures but decrease its self-diffusion coefficient of pure paraffin. Specifically at 323 K, the thermal conductivities have been increased by 22.6 % and 52.0 % by adding CuO and CNT into pure octadecane, respectively. Notably, distinct mechanisms of the thermal conductivity enhancements induced by CuO and CNT have been observed. The presence of CuO nanoparticles changes the conformation of octadecane molecules from linear to curved state but exhibits minimal influence on the molecular arrangement. In contrast, the incorporation of CNT not only makes the molecular conformation of octadecane more stretched but also facilitates a hierarchical crystal-like arrangement. Both CuO and CNT nano-additives contribute to the formation of a dense interfacial layer, with the layer showing a more ordered structure for CNT. It is concluded that, for paraffin/CuO composites, the increased collision frequency of particles within the dense layer is likely the main reason for the enhancement in thermal conductivity. Whereas for paraffin/CNT composites, the formation of an ordered crystal-like arrangement of octadecane molecules near the interface might be responsible for the thermal conductivity improvement.