Predictions of the complex annual cycle of temperature changes in a lake or reservoir are necessary if proper water quality control is to be achieved. Many lakes and reservoirs exhibit horizontal homogeneity and thus a time-dependent, one-dimensional model describing the temperature variation in the vertical direction is adequate. A discretized mathematical model was developed based on the absorption and transmission of solar radiation, convection due to surface cooling and advection due to inflows and outflows. The model contains provision for simultaneous or intermittent withdrawal from multi-level outlets and time of travel for inflows within the reservoir.