A dispersion system fluid can convect even if the dispersoid is a solid phase. Therefore, heat exchange performance can be improved while maintaining fluidity using a material with high thermal conductivity as the dispersoid. This study presents the melting performance evaluation results of a latent heat storage material with a carbon nanotube (CNT) dispersion system with high thermal conductivity, which enhances the thermal conductivity of the latent heat storage material and does not limit free convection. Increasing the thermal conductivity and enhancing the melting convection of the heat storage material result in increased latent heat storage speed. In this study, the thermal conductivity of the latent heat storage material was successfully increased by dispersing CNTs in the material. When 0.1% (in mass) of multi-wall CNT (MWCNT) was dispersed in a paraffin-based latent heat storage material, the shear stress increased by 1.5 times at a shear rate of 500 s^–1, while taking into account the potential effects of convective inhibition. Therefore, a latent heat storage experiment was conducted in a rectangular heat storage tank using the CNT dispersion composition ratio as a parameter. A rectangular vessel with a heated vertical surface was used for the latent heat storage experiment. The melting speed was determined by comparing the amount of latent heat stored in a CNT-dispersed latent heat storage material and a single-phase latent heat storage material sample. The experimental results show that the time required for the latent heat storage material to completely melt in the heat storage tank was the shortest for the single-phase latent heat storage material sample. However, the fastest melting progress was observed for the sample with 0.02% (in mass) MWCNT content in the melting rate range of up to approximately 40% in the tank. The results indicate that this phenomenon is caused by the difference in the melting rates in the upper part of the tank. The generated data are useful for determining the shape and heat transfer surface arrangement of the latent heat storage tank.