If (and I really don’t quite know how you’d do this) you could put long reach wells into these bodies and extract all the volatile content – probably as some sort of water-CO2 critical fluid – you might both cool and ‘defuse’ the rhyolite body. Indeed, these hydrothermal fluids are what give rise to many economic mineral bodies, so not only would you get a LOT of energy out of these boreholes, you might also get a lot of quite valuable minerals.

Issue is that you have to somehow put a borehole into temperatures of hundreds of degrees, stabilize it, and extract fluids without the whole works gumming up. And a blowout could be *ahem* interesting.

2C + 2 H2O –> CH4 + CO2

If the volatile is CO2, that becomes more difficult, but the solution is still to inject carbon. Then the carbon is removed as CO

C + CO2 –> 2 CO

The solubility of gases in magma goes as H2O, CO2, CH4, CO.

What is needed is to inject carbon, remove the gases, process them to recover the carbon and reinject the carbon while generating enough power to run the system.

I agree with Omega Centauri, that simple cooling would not be effective, you need to change the composition and remove volatiles, or add non-volatiles.

Adding silicon, is another way to modify the composition. Ferrosilicon is another way. It is denser than magma, would sink to where it would melt and the silicon and eventually the iron would react with the gases.

I would think the Lake Toba eruption roughly 85,000 years ago was at least as big as Yellowstone. Genetic evidence points to the human breeding population having been reduced to a few thousand at some time near then.

I used to think the way to stop eruptions would be longterm deep geothermal heat extraction, (probably taking a few hundred years to have an effect). But, since then, I’ve read that cooling of a magma body can cause the lower melting point constituents to freeze and separate gravitationally, leading to an eruption of the now changed composition magma. It may be that even with a thousand year warning, and huge resources that we still wouldn’t stop one.

Answering that for the result of step 1 is step 2.