Hi Andy,
Sorry, you're right! I didn't spend any time on thermal treatment.
My initial reaction is mixed. I think it is a great idea and the testing looks promising. I would have liked to see a study expanded into a whole hive situation and not the large "incubator" area described in the study. Perhaps this has been done and the results are published elsewhere? One problem I see is that bees like to brood around 32--35C (90--95F) and if you hold their temp at 40C (104F) it may 1) negatively impact brood health and/or 2) stress the bees in a hive trying to cool it off. I don't know this, but it is my initial thought. Now, if you did the thermal treatment at the end of a brood break, when you have no brood present and all the mites should be on adult bees, this might be a great behavioral-plus-treatment method. Also, comb might get pretty soft, so if it is new comb and full of honey, it might do better on plastic foundation or at least wired foundation, but that's only a minor issue.
I've never used poly hives and can't speak to them with experience but I wonder about temperature build-up in the summer and moisture build-up in the winter. Perhaps someone here has used them?
In sum, a promising idea. If you have the hives for it, say, ten hives, do this with five and do your regular treatments (if any) with the others, trying to keep variables constant and see how the mite counts fare year on year. You know, because we all have ten hives we can experiment with, right?
Sounds like a good report to give once you've tried it. I'm sure we'd all be glad for it to work well.