Rectangular shell-tube thermal storage systems have a wide range of applications in both industrial waste heat recovery and solar power plants. Mastering the heat transfer mechanism and improving the heat transfer efficiency can considerably enhance the energy-utilization. In this study, we experimentally investigated the dynamic thermal behavior of a visualized rectangular shell-tube type phase-change heat storage device containing natural convection, using paraffin wax as the phase-change material. Subsequently, the corresponding numerical simulation was completed. The two results agreed well, within a maximum error of ± 5%. In addition, the theoretical parameters of paraffin wax were examined experimentally. The impact of inlet temperature, flow rate of the heat transfer fluid, and the length-to-diameter ratio of the heat flow tube on the efficiency of the system was studied. It was observed that a rise in inlet temperature from 353 K to 363 K increased the melting rate by 21.43%. When the inlet flow rate was increased from 2 L/min to 5 L/min, the melting rate was raised by 16%. However, reduction in tube length-to-diameter ratio from G = 14 to G = 12 shortened the melting time of the PCM by 6.64%. The equation for the liquid phase fraction of the PCM with dimensionless Ste and Ra numbers was fitted. The research results have a specific guiding significance for utilizing rectangular shell-tube energy storage systems.