Cooling magma plutons and intrusions are the heat sources for hydrothermal systems in volcanic settings. To explain system longevity and observed heat transfer at rates higher than those explained by pure conduction, the concept of fluid convection in fractures that deepen because of thermal rock contraction has been proposed as a heat-source mechanism. While recent numerical studies have supported this half a century old hypothesis, understanding of the various regimes where convective downward migration of fractures can be an effective mechanism for heat transfer is lacking. Using a numerical model for fluid flow and fracture propagation in thermo-poroelastic media, we investigate scenarios for which convective downward migration of fractures may occur. Our results support convective downward migration of fractures as a possible mechanism for development of hydrothermal systems, both for settings within active zones of volcanism and spreading and, under favorable conditions, in older crust away from such zones.