The annual cycle of temperature changes in a lake or reservoir may be quite complex, but predictions of these changes are necessary if proper control of water quality is to be achieved. Many lakes and reservoirs exhibit horizontal homogeneity and thus a time-dependent, one-dimensional model which describes the temperature variation in the vertical direction is adequate. A discretized mathematical model has been developed based on the absorption and transmission of solar radiation, convection due to surface cooling and advection due to inflows and outflows. The mathematical model contains provision for simultaneous or intermittent withdrawal from multi-level outlets and time of travel for inflows within the reservoir. Heat transport by turbulent diffusion in the hypolimnion is neglected. (Modified author abstract)