The research work explores the impact of temperature on Silicon photovoltaic (PV) panels, considering Nigeria as a case study. It is found that high solar radiation in Nigeria increases the surface temperature of PV panels above 25 °C of the optimal operating temperature. The redundant energy gain from solar irradiance creates heat at the rear of solar panels and reduces their efficiency. Cooling mechanisms are therefore needed to increase efficiency. In this study, we demonstrated a unique hybrid system design employing a heat exchanger at the back of the panel, with water circulated through the back of the PV panel to cool the system. The system was simulated using TRNSYS at three locations in Nigeria—Maiduguri, Makurdi, and Port Harcourt. The results of the peak annual electrical power output in Maiduguri give a power yield of 1907 kWh/kWp, which is the highest, due to a high solar radiation average of 727 W/m2 across the year. For Makurdi, the peak annual electrical power output is 1542 kWh/kWp, while for Port Harcourt the peak power output is 1355 kWh/kWp. It was observed that the surface temperature of Polycrystalline Si-PV was decreased from 49.25 °C to 38.38 °C. The electrical power was increased from 1526.83 W to 1566.82 W in a day, and efficiency increased from 13.99% to 15.01%.