Magma intrusions in the Earth’s crust cool over time, but they do not cool in isolation. Circulating groundwater often forms a hydrothermal system above the intrusion, drawing out heat and controlling how quickly the magma solidifies. This process shapes not only the thermal structure of the crust, but also how long magma can stay molten and potentially eruptible. In this talk, I show how numerical models that combine fluid flow and heat transfer from magma help us understand this coupling between magmatic and hydrothermal systems. I explore how permeability, fluid salinity, and mineral precipitation affect fluid circulation and the efficiency of heat extraction. These processes explain why some magmatic systems show sharp thermal gradients and cool rapidly, while others evolve slowly and remain in a potentially eruptible state. Understanding this interplay is important not only for volcanic hazards, but also for the development of high-temperature geothermal resources that depend on tapping heat near magma.