In radial distribution systems, the significant concern of power loss is mainly attributed to the high R/X ratio. The resistance of branches is notably affected by temperature changes resulting from these losses, traditionally remaining constant within the system. This paper introduces an innovative Weather-Influenced Power Flow method, specifically designed to accurately calculate real power losses in distribution systems. The objective is to determine precise power losses and enhance the value of power flow solutions by considering the impact of weather conditions on branch resistance. This approach aims to incorporate weather conditions into the solution process for radial distribution systems. The effectiveness and feasibility of the proposed method are demonstrated through testing on the IEEE 33-bus system. A comparative assessment with forward/backward power flow analyses in radial distribution systems reveals a substantial difference in power loss, resistance, and bus voltages when resistance is treated as a constant parameter compared to being influenced by weather.