Termites can dig very deep. The final inspection went 30 meters down. Burning down 30m into the earth would require something far beyond what "onsite burning" usually involves. (Hence the "small subterranean fusion bomb" comment from kingcharles.)
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It wouldn't remove the termites, but it would remove the surface structure ... which should make it easier to do the subterranean work. Instead they wouldn't let the homeowners modify the house.
Isn't that 30 meters one of the dimensions of the surface area that was inspected?
If they actually inspected 30m into the Earth, they'd have plenty of opportunity to kill everything in the way as they did it.
I sometimes have very weird and destructive thoughts, but I have often wondered if it were possible to take thermite and pack it, make it stable and rigid somehow, enough that it could be made into a long rod, like rebar, suitable for pounding into the earth. Then you surround your nest or whatever with a bunch of rods, run one through the middle, set them alight and let them just burn down however many yards.
Thirty meters, though ... whew.
Outside of sci-fi and some very arid environments, rapid extreme heating of large quantities of soil will produce big steam explosions. Which might spread some relatively unheated, termite-laden clods of earth over a wide area.
In a different context (limited quantities of soil with extremely heavy chemical contamination), I have seen serious proposals to drive heavy electrodes deep into the soil, gradually apply very large currents (avoiding steam explosions), and let the heat & electricity destroy the contaminants in-place.
What about pressure? Would it be possible to apply either a violent pressure wave, or some sort of compaction technology to basically crush everything 30m down?
If the termites could be living ~30m down...pressure at that depth, just from the weight of the overlying soil, is already about what you'd experience under a 300m-tall skyscraper. So suitable crushing equipment might be rather large and expensive. A violent-enough pressure wave would require a very large explosion...let's just say that senior political leaders would have to sign off, and those folks would smell too much potential for career-ending scandal and ridicule to do so.
How about microwaves? If the soil is moist, perhaps microwaving the area could sterilize it thermally. Slower rate of heating should prevent explosions.
Drilling and filling would probably work better.
I guess by the time you got enough thermite in the ground it wouldn't be very efficient.