Im not 100% sure if this might address some of your issues.. (not sure I understand most of it! but...)
https://fireinabottle.net
After wading through a mass of verbiage, came to the point where he talks about burning off fat as heat
"This allows you to turn your stored fat into heat rather than stored chemical energy! You can just burn off your stored calories!" Note ATP is the chemical energy.
That is all he says about the process. Having re-read the section a couple of times, it is apparent but implied that the heating is occurring in the brown fat cells, which is actually their job as originally designed by the maker. But in other places he mentions it in relation to mitochondria which again I think is incorrect,
He also mentions the mitochondria handling saturated fats. Now most cells in the body are mitochondria, and they are simple furnaces that can just about deal with pyruvate and citrate but in actual fact only burn ATP. They can munch on glucose, some basic ketones, and short-chain fatty acids, but nothing complex. It seems mitochondria would not be able to deal with long or medium-chain fats, which must be enzyme zapped outside it.
Most papers I have seen say that it is the brown fat cells that heat the body. Mitochondria do generate some heat while actually storing or retrieving glucose into glycogen, and also when ATP is oxidated by use. I cannot confirm heat while idle or while fat burning. The references I found on Wikipedia say that brown cells produce non-shivering thermogenesis and mitochondria muscle cells by shivering. There is one controversial study in PLOS One that claims that mitochondria run themselves at 50C but this is heavily refuted elsewhere. Again the link to insulin and fat burning is not explained except that it happens????