I'm so sorry you're going through this awful situation.
Do you actually have a fever? Or is your skin seemingly hot but your internal temperature is normal?
You need better doctors. I would suggest you call the Mayo clinic and ask for help. This is the kind of mysteries they solve.
My best guess is, this is an overactive thyroid issue. When they test for thyroid, they test 4 levels and if each of the levels are within "normal" they declare it's not a thyroid problem. But thyroid hormones are in balance - and if one is "high normal" and others are in "low normal" you could die from thyroid issues while your doctor says your levels are fine.
Best wishes, and prayers for your healing.
So I googled this - and found this is recognized in Eastern cultures, and has been forever. It's called "empty heat". You might want to google it.
The whole point of this post is to tell you it's not uncommon, other cultures recognize it, and I'm sorry your doctors have completely brushed you off.
You deserve answers.