A one-dimensional transient heat conduction model to describe the decay of the thermocline in a stratified water tank is presented. The problem is formulated as an initial boundary value problem and the resulting governing equations in the fluid and in the storage wall are solved numerically to obtain the temperature profiles in the wall and the fluid. The formulation considers the axial conduction of heat, both in the fluid and in the solid wall. The mixing parameters introduced in the boundary conditions at the top and bottom of the tank in the fluid region account for mixing due to inlet and outlet streams with the stored fluid. The model is applicable to the storage of both hot and chilled water. The model is validated with experimental data from the literature. The parameters that influence the operation of a stratified thermal energy storage for both heat and cool storage are examined.