Flat-plate solar collectors are crucial in Borehole Thermal Energy Storage systems for bridging the gap between renewable energy supply and consumer heat demand. Because most studies rely on idealized models, this work develops a Python-based transient mathematical model of a "solar collector–heat exchanger" system using energy balance equations and real commercial SchücoSol collector specifications. With this validated model, a parametric and sensitivity analysis (±20%) evaluated how daily efficiency is impacted by optical efficiency, heat losses, heat exchanger transfer coefficient, fluid mass flow rate, and ambient temperature. Results demonstrate that ambient temperature, optical efficiency, linear heat losses, and heat exchanger characteristics most significantly influence efficiency. These findings quantitatively assess the impact of design and operating parameters, offering practical recommendations for designing and optimizing real seasonal thermal energy storage systems.