Phase change material (PCM) is employed to enhance the thermal energy storage capacity of a building integrated photovoltaic thermal (BIPV/T) system. For this purpose, the best thickness of PCM is found using the dynamic multi-objective optimization (MOO), in which the performance throughout a year with real-time data is taken into account. In addition to the annual thermal energy storage capacity (AES), the annual energy (electricity) production (AEP), as well as payback period (PBP), the levelized cost (LCOE), and annual carbon-dioxide emission reduction (ACDR) are considered as the objective function to obtain a favorable condition from all the energy, economic, and environmental (3E) perspectives. MOO is done for a residential building in Tehran, Iran, by employing numerical modeling for system simulation and the combination of TOPSIS and NSGA-II techniques to determine the final optimal solution. According to the results, the best PCM thickness is 77.2 mm. Compared to the base condition, in which air is used as the material for energy storage, using PCM with the optimum thickness is accompanied by 22.24%, 9.93%, 17.69%, and 9.59% improvement in AES, AEP, ACDR, and LCOE, respectively. Moreover, PBP in the optimum condition is 3.321 years, which shows that utilizing the results of MOO is economically justifiable.