The heat transfer characteristics for the case of laminar flow through a hexagonal channel have been determined for the following conditions: The uniform heat flux on any one side of the hexagon is identical to that on the opposite side, and may be equal to or different than those on the two adjacent sides; both the velocity and temperature profiles are fully established; the heat transfer from the walls may or may not be accompanied by simultaneous internal heat generation in the flowing fluid. Fundamental temperature solution and equations are presented which may be used to predict the temperature field, or to calculate the difference between local wall temperature and the bulk fluid temperature for a variety of cases. Methods of predicting the variation of local wall temperature are illustrated for several typical cases, including the case of uniformly distributed wall heat flux. For the latter case, it was found that appreciable temperature variation exists along the periphery of the hexagon. The circumferential variation of the local Nusselt number and the mean Nusselt number are also reported, with and without internal heat generation.