A numerical study of the velocity and temperature distributions that arise in a water body due to a thermal discharge such as that in a heat rejection or a sensible energy storage system, has been carried out. The time‐dependent distributions, as well as the steady‐state solutions, have been obtained by the use of the alternating direction implicit method for the coupled vorticity transport and energy equations. The numerical procedure employed is outlined, indicating some of the salient features and problems that arise. The numerical scheme is employed for the study of various flow configurations and the dependence of the flow on the governing parameters, particularly on the mixed convection parameter, is determined. The results obtained are discussed in terms of the physical mechanisms involved. The uncoupled problem, for an unheated discharge, is also considered and the coupled nature of the equations is evident in the results obtained for heated discharges. The relevance of the results obtained to the recirculating flow of interest in heat rejection and energy storage is discussed.