Traditional power flow algorithms, including Newton-Raphson (NR) based methodsand backward-forward sweep (BFS) based techniques, consider conductor resistance as a fixed quantity predetermined for some assumed combination of ambient conditions (weather, soil temperature, etc.) and loading that imply a certain conductor temperature. However, during the course of an iterative power flow algorithm, the calculated current, and thus conductor temperature, and consequently conductor resistance are changing at each iteration. Therefore, dependent on the actual ambient and loading conditions of a system, there can be a non-negligible temperature related error embedded in a conventional power flow solution. Some work has been done to address this in transmission systems with NR-based temperature-dependent power flow techniques, but the literature is almost silent on the effect that the consideration of conductor temperature may have on power flow for distribution systems. Distribution systems have unique characteristics including radial topologies, high R/X ratios, smaller quantities of delivered power, shorter line segments, and an inability to make assumptions about balanced loading that make them distinct from transmission systems and often require non-NR based solution methods to solve the power flow problem, such as BFS techniques. In this work, a temperature-dependent three-phase power flow algorithm for radial systems is proposed. The proposed algorithm couples the electrical and thermal characteristics of overhead and underground lines for a more accurate solution to the power flow problem. This method is capable of accounting for the particularities and requirements of modeling distribution systems as distinct from transmission systems, including untransposed lines, unbalanced loading, three-phase transformer and voltage regulator models, and constant current, impedance, and power loads. The line phase impedance matrices are updated at each iteration of the algorithm with the calculated resistance as derived from the calculated conductor temperature. The proposed method is tested against standard IEEE test feeders using real world weather and soil temperature data sets, and the results are compared against the accepted benchmarks with respect to system nodal voltage profile, real power loss, and degree of voltage unbalance.