The present study proposes a Quonset-type greenhouse integrated with a thin-film photovoltaic thermal (GiPVT) system combined with an earth-air heat exchanger (EAHE) for crop cultivation in harsh hot climate conditions. A periodic thermal model in terms of input climatic and design parameters has been developed to evaluate the GiPVT system’s thermal performance. This model is based on the energy balance equations of the GiPVT system, and it calculates PV roof temperature, greenhouse air temperature, and plant temperature for a given climatic data, i.e., solar irradiation and ambient air temperature. Furthermore, the thermal load leveling for the GiPVT system is determined to assess the thermal comfort status within the enclosed space of the system. The results indicate that EAHE successfully reduces greenhouse air temperature and increases the thermal comfort level inside the GiPVT system. Corresponding to the optimum flowrate of 0.5 kg/s, the maximum temperature of the plants and greenhouse is reduced by 20 °C and 21 °C, respectively. Moreover, the present GiPVT system produces 29.22 kWh of electrical energy per day, making the system self-sustainable.