A quonset-type Greenhouse integrating Thin-film Photovoltaic (GiTPV) system is proposed and designed to facilitate the growth of plants under harsh cold climatic conditions. The proposed GiTPV system is coupled with an Earth-Air Heat Exchanger (EAHE) that utilizes shallow-depth geothermal energy to enhance the self-sustainability of the system. Such a greenhouse system is subjected to climatic parameters that vary periodically over 24 h; hence its performance should be investigated under dynamic periodic conditions. The present investigation develops a periodic thermal model based on energy equilibrium equations for evaluating the performance of the GiTPV system coupled with an EAHE. The results indicate that EAHE provides heating inside the GiTPV system’s enclosed space during the off-sunshine hours and reduces the room air temperature fluctuations resulting in better thermal comfort. The greenhouse air and plant temperatures are increased by 5 °C and 4 °C, respectively, for an airflow rate of 0.5 kg/s flowing through the EAHE. Furthermore, the GiTPV system produces 15.3 kWh of electrical energy per day, making the system self-sustainable for the considered cold climatic condition.