Can you stop a volcano from erupting by cooling the magma beneath it?
Probably not. Volcanoes don’t necessarily erupt because of the temperature of the magma in the magma chamber, they erupt because of the expulsion of dissolved volatile gases in the magma, or because of an abrupt upwelling of excess magma into the chamber which causes it to overflow and erupt. Explosive eruptions can also result from natural plugging of the vent, with a build up in pressure resulting in explosion. It would take an immense amount of water to cool a magma chamber, and the risk of allowing the cooling water to come into contact with the magma and therefore cause a phreatomagmatic explosion would be great. Many volcanic areas use geothermal power which relies upon water being heated by a magma reservoir. Large volumes of water are used in this process, and the impact over time upon the temperature of the magma is nil.