The most general models for glacial hydrologic conduits include an energy equation, wherein a heat transfer coefficient controls the rate at which heat generated by mechanical energy dissipation is transferred to conduit walls, producing melt. Previous models employ heat transfer coefficients derived for engineering heat transfer problems, where heat is transferred between the walls of a conduit and a flowing fluid that enters the duct at a temperature different from the wall temperature. These heat transfer coefficients may not be appropriate for glacial hydrologic conduits in temperate ice, where the flowing fluid (water) and conduit walls (ice) are at almost the same temperature, and the heat generated by mechanical energy dissipation within the flow is transferred to the walls to produce melt. We revisit the energy transport equations that provide a basis for the derivation of heat transfer coefficients and highlight the distinctions between the heated walls and dissipated energy heat transfer cases. We present computational results for both cases across a range of Reynolds numbers in circular conduit and sheet geometries. For the heated walls case, our results are consistent with the widely used Dittus-Boelter heat transfer correlation, which has been used in previous glacial conduit models. We show that the heat transfer coefficient for transfer of heat generated by mechanical energy dissipation to conduit walls is smaller than that calculated using the Dittus-Boelter correlation by approximately a factor of 2.