The contents of the paper are based on an extension of the analogy between heat and momentum transfer. Following the suggestion of von Kármán (9), the turbulent-flow field is divided into a laminar sublayer, a buffer layer, and a turbulent core. The thermal resistances of the laminar sublayer and the buffer layer are calculated as in the paper by Boelter, Martinelli, and Jonassen (1), but the thermal resistance of the turbulent core is re-evaluated for very low values of the Prandtl modulus (molten metals) by considering the simultaneous transfer of heat by molecular conduction and eddy diffusion. The relative importance of the thermal resistances of the laminar sublayer, buffer layer, and turbulent core is discussed and the temperature distribution in the fluid is evaluated for various magnitudes of the Prandtl modulus. It is demonstrated that the unit conductance for convective heat transfer is proportional to the square root, rather than the first power, of the friction factor. A tentative analysis is made of the data of Cope (19) for heat transfer in rough pipes.