Summary In this study, a multicriteria optimization is developed for a hybrid building integrated photovoltaic/thermal (BIPVT) system with a sensible rotary heat exchanger (SRHX) for both heating and cooling purposes. The BIPVT system is considered with and without considering the glass cover. Both the heat and electricity produced by the BIPVT‐SRHX system are determined according to the energy and exergy phenomena. The objective functions aimed to be maximized are the annual total amount of generated energy and exergy. The length and depth of SRHX, geometrical parameters of PV modules, and the air mass flow rate are the parameters considered in the optimization. The results reveal a high amount of produced energy for the optimized design; however, the total amount of generated exergy is low. The system with the glass cover shows a higher amount of gained heat and less generated electricity compared with the system without the glass cover. The total energy produced by the system with and without the glass cover is about 227 and 220 MWh, respectively, and the total produced exergy by the systems with and without the glass cover is 1207 and 1585 kWh for the optimized design, respectively. The effect of setting a glass cover on the photovoltaic panels belonging to a building integrated photovoltaic thermal system on the energy and exergy performances of a hybrid system consisting of a building integrated photovoltaic/thermal system and a sensible rotary heat exchanger is investigated numerically. The outcomes are compared with those of the hybrid system incorporating an uncovered building integrated photovoltaic/thermal system. For this purpose, the multi‐objective optimization is used to determine the optimal energy and exergy performances of the covered and uncovered hybrid systems, then the performances of optimal units are compared for climate of Kermanshah, Iran. Glass cover has a considerable effect on the energy and exergy performances of hybrid system, and when designing the hybrid system, its impact must definitely be considered.