The cooling system is also how you extract energy from the reactor. Anything you do to extract energy will have this effect; if it didn’t you’d have a perpetual motion machine.
The cooling sounds like a side-effect then. The goal isn't to cool for the sake of it. You want the energy out of it. If you just want a cooling system you could spray water onto it and let the steam escape. That'd be an effective cooling system. What people really mean is that they want to usefully extract the energy.
