One approach to storing latent heat in large quantities is through PBSS (Packed bed storage system) with spheres filled with PCM (Phase Change Materials). In these storage systems, an HTF (heat transfer fluid) flows over the spheres. So, both the sphere wall temperature and the heat flux can vary depending on the geometric conditions of the bed of spheres, the PCM thermodynamic conditions, and the HTF thermal conditions. Thus, this work aims to verify the influence of the thermal conditions of the external flow on the PBSS filled with PCM in the melting process. Cases with variable heat flux as well as uniform temperature and uniform heat flux conditions were tested. Three sphere positions, 4 sphere spacing ratios (blockage ratio), and three temperature differences between HTF and PCM phase change temperature were also analyzed, for two external flow directions (upstream and downstream), totaling 74 different configurations. The study found that the uniform temperature condition resulted in a 33 % faster total melting time than the uniform heat flow condition. Additionally, the upstream flow showed a total melting time that was approximately 24 % shorter than the flows in the opposite direction. The relationship between the total melting time and the temperature differences was found to be non-linear. Moreover, the blockage ratio showed a non-linear dependence with total melting time. The configuration with a blockage ratio of 1.125 demonstrated the shortest total melting time, with values on average 22.4 % shorter than the blocking ratio of 0.550, which had the longest melting times. These results demonstrate that optimizing external flow thermal conditions is crucial for improving the performance of PBSS with PCM-filled spheres in large-scale latent heat storage systems.