The structural and architectural elements of building-integrated photovoltaic-thermal (BIPVT) systems are made up of photovoltaic (PV) modules and these are required to be fixed at an optimum inclination angle for generating maximum exergy. This work presents an attempt to determine the amount of exergy generated by an optimally inclined double-storied BIPV thermal system by considering the actual cyclic nature of insolation, surrounding air temperature, PV cell temperature, intermediate slab temperature, and the chamber temperature. The insolation value, which is computed by an anisotropic sky model along with these cyclic variables, is used for solving the set of governing differential equations for evaluating the exergy of the system. Other influencing parameters of the BIPV thermal systems such as air changes in both chambers, packing factor of PV module, the orientation of PV module, and thickness of the intermediate slab are considered for finding its effect on the total exergy of the system. Numerical results show that for packing factor more than 0.6, there is no significant change in total heat exergy with respect to the inclination angle. For packing factor more than 0.3, the generation of electrical exergy exceeds the heat exergy, and the overall exergy of BIPVT system decreases with rise in packing factor (βm) up to 0.3 and then rises nonlinearly.