I'm the opposite if anything, I get sweats and chills, often my stomach is literally burning hot to the touch when I am on the loo, but I - usually - only feel cold after a bout of diarrhea. I have always assumed that the amount of fluid lost - quite a considerable amount when you think of it as a percentage - is enough to clobber the electrolyte balance in the body, which makes keeping the body at an even temperature even harder than it would be during a normal infection or fever.
My remedy is drinking orange juice (to restore the electrolytes) and cups of hot non-caffeinated drinks (to restore warmth and fluid) and most effective of all, bed and sleep.
If it isn't electrolytes, then it may well be simply that the gut has such a big effect on neurotransmitters, and has so many major nerves connected to it, that the upset is enough to affect the autonomic nervous system. That wouldn't surprise me, it would certainly explain why sleep calms things down - it's like rebooting a computer.
Doesn't half feel lousy though, does it ?