> Yellowstone has erupted 3 times in the past approx. 2.1 million years, with total ejected ash approaching 10^15 kg. While the heat energy associated with this ash is some 10^23 J, this averages to only approx. 1.5 GW continuous magmatic thermal power input to the volcano over the span of these eruptions, and is well within the capacity of humans to safely introduce heat into the environment – a typical electrical power plant commonly rejects more heat than this. However, this assumes that heat is provided to the magmatic system in a steady state manner, which is almost certainly not valid, although the degree to which it is invalid is unknown.
...which, by my lights, sounds far too much like specifying "able to withstand the local average wind speed" in the building code for Hurricane City, Florida.