Enhancing heat transfer during the charge and discharge of solar thermal storage tanks is an ongoing technical challenge. The types of thermal storage systems considered in the present study comprise an immersed heat exchanger at the top of a solar thermal storage fluid. The discharge process of a thermal store with specified dimensions is numerically simulated over a range of Rayleigh numbers, 105 < RaD <107. The immersed heat exchanger is modeled as a two-dimensional isothermal cylinder which is situated near the top of a water-filled tank with adiabatic walls. An adiabatic shroud whose shape is parametrically varied is placed around the cylinder. In addition, the shroud is connected to an adiabatic baffle situated beneath the cylinder. Nusselt numbers are calculated for different shroud shapes at different Rayleigh numbers. Results show that the shroud is effective in increasing the heat transfer rate. Optimal shroud and baffle geometries are presented as well as qualitative flow results.