It will defiantly do something! You would have to be very careful not to set light to the shed of course. If you do try that then do it in the morning when you can keep the hens out of it all day and be sure that when they go to roost that evening it isn't still smouldering ready to catch light.
I would be a bit more strategic about it as well. The place you cant get at very easily (and also one place where the mite are probably hiding) is in the roof. Heat rises so you could spend half an hour gently raising the roof temperature until its too hot to comfortably touch. You then know they are defiantly not in the roof and that would be a big step forwards. Paint diatom slurry all around the inside roof edge so they cant just move back in.
If there are big gaps you cant take apart lower down then you can give them a quick blast and know the heat is travelling through but with smaller gaps you wouldn't get the heat in there before you set light to the timber. The heat gun is better in this regard as you can blow the hot air through the cracks.
Another way would be to use the torch as a general heater (or use a safer form of heater) to raise the whole thing above 55 degrees. Unlikely to heat the floor effectively though
You will still need to use the diatom to discourage a new infestation but would be starting from zero again at least
Please be careful! For both you and your chickens sake. If the HSE are reading this they will be having kittens!!!
You have just found out you have red mite. You've had them all summer and been blissfully unaware so all you need to do is put some measures in place to bring the population back under control. Controlling the population of red mite is, unfortunately, just a part of chicken keeping that is as ongoing as cleaning out. Although wiping them all out in one holocaust may seem like the thing to do it is more important to just get into the business of discouraging them. What you have done already will have already had some effect it just needs keeping up.
...There are so many reasons not to operate a weed torch in a shed that it would require several sheets of A4 to list them.
Oxygen depletion, gas bottle temperature, feed pipe temperature, flashover!!!!! etc. etc. etc.....
... says the man who is currently re-pointing the upstands on his own roof...