In hot dry regions, photovoltaic modules are exposed to excessive temperatures, which leads to a drop in performance and the risk of overheating. The present numerical study aims to evaluate the natural air cooling of PV modules by an inclined chimney mounted at the back. The basic equations were solved using the finite volume method. The validity of the model is verified by comparison with the data available in the literature. Thermal and dynamic flow patterns are analyzed for a variety of parameters: Rayleigh numbers from 102 to 106, PV panel tilt angle from 15° to 90°, and channel aspect ratios from 1/20 to 1/5. A critical aspect ratio has been determined to minimize overheating of the PV module. According to the computational results, the tilt angle and modified Rayleigh number increase the mass flow rate and mean Nusselt number. The overheating zone with maximum temperatures is located in the upper part of the photovoltaic panel. The addition of an extension to both channel’s inlet and outlet was found to improve the cooling of the photovoltaic panels; however, only the extensions downstream of the channel are truly effective. The critical lengths at which channel performance improves significantly were identified by examining the impact of longer extensions on channel performance. Increasing the extension length from 0 to 3H improves the mass flow rate by 65%, the average Nusselt number by 13.4%, and leads to an 11% decrease in maximum temperature when Ra* = 106. This cooling technique is particularly promising for hot dry regions where water is scarce.