This paper presents a comprehensive analysis of the heat transfer during the melting process of a high-temperature (>800 °C) phase-change material (PCM) encapsulated in a vertical cylindrical container. The energy contributions from radiation, natural convection, and conduction have been included in the mathematical model in order to capture most of the physics that describe and characterize the problem and quantify the role that each mechanism plays during the phase-change process. Numerical predictions based on the finite-volume method have been obtained by solving the mass, momentum, and energy conservation principles along with the enthalpy porosity method to track the liquid/solid interface. Experiments were conducted to obtain the temperature response of the thermal energy storage (TES) cell during the sensible heating and phase-change regions of the PCM. Continuous temperature measurements of porcelain crucibles filled with ACS grade NaCl were recorded. The temperature readings were recorded at the center of the sample and at the wall of the crucible as the samples were heated in a furnace over a temperature range of 700–850 °C. The numerical predictions have been validated by the experimental results, and the effect of the controlling parameters of the system on the melt fraction rate has been evaluated. The results showed that the natural convection is the dominant heat transfer mechanism. In all the experimental study cases, the measured temperature response captured the PCM melting trend with acceptable repeatability. The uncertainty analysis of the experimental data yielded an approximate error of ±5.81 °C.