Large impact events, like the one that formed the Sudbury crater in Ontario, Canada, at 1.85 Ga, significantly increase the temperature of target rocks. The heat sources generated by such an impact event can drive the circulation of groundwater, establishing a hydrothermal system. We report on the results of numerical modeling of postimpact cooling with and without the presence of water at the Sudbury crater. A hydrothermal system is initiated in the annular trough between the peak ring and final crater rim, perhaps venting through faults that bound blocks of the crust in the modification zone of the crater. Although circulation through the overlying breccias may occur in the center of the crater, the central melt sheet is initially impermeable to circulating fluids. By ~105 years the central melt sheet crystallizes and partially cools, allowing fluids to flow through it. Host rock permeability is the main factor affecting fluid circulation and lifetimes of hydrothermal systems. High permeabilities lead to a rapid system cooling, while lower permeabilities allow a steady transport of hot fluids to the surface, resulting in high surface temperatures for longer periods of time than cooling by conduction alone. The simulations presented in this paper show that a hydrothermal system at a Sudbury-sized impact crater can remain active for several hundred thousand to several million years, depending on assumed permeability. These results suggest that a hydrothermal system induced by an impact event can remain active for sufficiently long periods of time to be biologically significant, supporting the idea that impact events may have played an important biological role, especially early in Earth's history.