I don't think that there's much you can do......If it's the same as I had, you're hot yet freezing at the same time.....Good old hormones!
I wake up sweltering hot and wet from sweat, but not cold. Are you cold because of being hot and sweating and then it cools you off too much? Sorry, just trying to get a better understanding.
Good idea on the fan, Joy---I'm gonna start doing that (i'm running out of clothing to remove! lol)
Maybe you could try keeping a fan on you at night? Or wearing less when you go to sleep? Hope those suggestions help!