To satisfy the hot water demand of any building, a suitable thermal storage device must be added to a Photovoltaic thermal system (PVT) to address the time lag between the supply and demand of thermal energy. In this study, a nanofluid-cooled photovoltaic/thermal system retrofitted with a phase change material (PCM)-based thermal battery is designed to meet a portion of the electrical and thermal demands of a residential building for the climate of Dhahran, Saudi Arabia. Daily and yearly performance evaluation of the system is analytically performed through Engineering Equation Solver (EES) software and compared with the performances of a nanofluid-cooled PVT system without thermal storage and an uncooled PV system together with an economic assessment of the proposed system. A comparison of systems with and without thermal storage shows that the introduction of a PCM-thermal battery has made it possible to meet some of the building's thermal load but at the cost of reduction in the system's electrical and thermal outputs. The proposed system, however, shows an 11.7% improvement in its electrical performance over an uncooled PV system. The addition of thermal storage has made it possible to cover up to 27.3% of the residential thermal load along with 77% of the residential electrical load.