The article deals with the experimental and numerical thermal-flow behaviours of a low-temperature Phase Change Material (PCM) used in Thermal Energy Storage (TES) industrial applications. The investigated PCM is a composition that consists of a mixture of paraffin wax capsuled in a melamine-formaldehyde membrane and water, for which a phase change process occurs within the temperature range of 4 °C to 6 °C and the maximum heat storage capacity is equal to 72 kJ/kg. To test the TES capabilities of the PCM for operating conditions close to real ones, a series of experimental tests were performed on cylindrical modules with fixed heights of 250 mm and different outer diameters of 15, 22, and 28 mm, respectively. The module was tested in a specially designed wind tunnel where the Reynolds numbers of between 15,250 to 52,750 were achieved. In addition, a mathematical model of the analysed processes, based on the enthalpy porosity method, was proposed and validated. The temperature changes during the phase transitions that were obtained from the numerical analyses in comparison with the experimental results have not exceeded 20% of the relative error for the phase change region and no more than 10% for the rest. Additionally, the PCM was examined while using a Scanning Electron Microscope (SEM), which indicated no changes in the internal structure during phase transitions and a homogeneous structure, regardless of the tested temperature ranges.