First the bees do not breath through their throats, they do not have lungs, but take air in to the trachea tubes Their are 2 and they are air tubes that take Oxygen directly to the bees muscles. They do not have a blood to transfer oxygen like mammals. Acarapis woodi Known to beekeepers as the Tracheal mite occupies the trachea of the bees, breeds there and while it develops the mite defecates in the trachea. This effects the bees ability to get oxygen to the muscles, causing the bees live to be shortened. The reason you do not heat of the trachea mite much is that with the introduction of Varroa with it being a much bigger mite, beekeepers needed to use way stronger chemicals for treatment. All the chemical treatments that kill varroa also easily kills Acarapis woodi. So when we treat for varroa we have also treated for the trachea mites if chemicals where used.
If you are treating Varroa by natural non chemical methods, by brood breaks of drone brood culling. Then the trachea mite is not being controlled and another means of mite control needs to be applied to control these mites so they do not build up and kill the colony. The damage done to the bees by the mites is what happens to the winter bees, the bees that need to have an extended life to get the colony through to spring build up.
Grease patties are a non chemical treatment that worked for trachea mites, it was easy, safe to use, didn't need as much government approval as it was all human consumption approved products went into making the patties. It kills the mite by suffocating it. The bees would try to clean up the grease patty by collecting the sugar out of it and in the process would spread a fine film of oil on themselves, The mites would also get the fine oil coating on them but due to their size (need a 40 X 10 power microscope to see them) They wood be killed.
Think of it as you put a small amount of bubble bath in your bath and soak in it with no ill health effect. You put the same amount of a soap in a spray bottle and use it on your plants and it kills aphid's. but we can still eat the product that it was sprayed on. It is concentration to body mass.