Radial temperature distributions within the cores of heterogeneous circulating-fuel reactors having elementary channel and circular pipe geometries are described mathematically; uniform and nonuniform radial volume-heat-source distributions are considered. Solutions for cores with uniform volume-heat source distributions are tabulated so that detailed radial temperature profiles can be determined within fuels which are being uniformly cooled at the core walls. A derivation is presented which describes the heat transfer within a reactor core when walls are being non-uniformly cooled along its length; volume heat sources also exist within the core walls and coolant.