One possible answer is that once we have CFS, mainting homeostasis for lots of things, inclduing temeperature, becomes much harder. CFS is largely a neural disease and all those bits have to work right to get proper autonomic function, which is how we achieve homeostasis.
not very satisfactory thought since that predicuts any extreme would be difficult and its definitely heat in particular that 's a trigger. But even in MS, there is no good satisfying explanation for why heat makes demyleniated neurons worse.
more hand waiving is that seems to go along with inflammation. maybe heat triggers mast cells and floods of inflammtion. Any mast cell issues? (sorry i've got mast cell on the brain right now).
i have heat issues too- especially sun though for me. Took me so long to realize that that i wasn't feeeling hot from the sun, but sick. and took me just as long to realized that everyone wasn't feeling this - i thought was normal...
have you looked for SSA antibodies? but that's neither necessary nor sufficient and might not even go along with the feeling sick anyway.