Phase-change materials (PCMs) utilize the latent heat absorbed and emitted during their phase change and are used in many thermal applications. Studies have investigated the melting process of PCMs filled in a rectangular cavity and have determined that the melting of PCMs in a closed cavity is considerably affected by natural convection in the melted PCMs. Therefore, a detailed understanding of the heat-transfer mechanism that governs the melting of PCMs is required to maximize the melting rate, which influences the thermal performance of storage systems that use PCMs. To this end, we develop a visualization technique using high-performance infrared thermography to evaluate the natural convective heat transfer while melting n-octadecane in a rectangular enclosure heated from below. This technique provides a novel characterization of the complicated natural convection during the melting of PCMs in terms of its spatio-temporal variations, the resulting convective heat-transfer characteristics, and the relationship with the morphology of the solid–liquid interface. To investigate the effects of heating conditions and inclination angles of the enclosure on the heat transfer characteristics, we performed experiments to measure the spatio-temporal variation of heat transfer coefficient of the heated surface at different levels of input heat flux (Stefan numbers Ste = 1.1, 2.4, and 4.2) and inclination angles (0° and 20°). We also captured the solid–liquid interface by a digital camera and performed an image processing using MATLAB to evaluate the melting behaviors of the PCM. We determined that the heat-transfer mechanism varies continuously based on melting stages of the PCM, and it is considerably affected by the variations in the input heat flux and inclination angle. In addition, we obtained the scaling law of the Nusselt number and the Rayleigh number for the experiments at each Ste and θ and found to be different values of the Nusselt number depending on the tested conditions. These variations were attributed to the changes in the number of ascending and descending plumes, solid–liquid interface, convection structure, and supply of cold fluid at each melting stage. Thus, our method enables the visualization and quantitative evaluation of important dynamical transitional behaviors of convection roll structures attributed to the continuous melting (e.g., formation, merging, and fluctuation of convective plumes). These experimental results can be used to enhance the understanding of the complicated phenomena and validate numerical simulations related to the melting of PCMs.