I'm guessing it's just because our core body temp drops a full degree as we start to fall asleep before returning to normal that if our temp is already low, our body shivers to bring it up to normal. I also have a normally low blood pressure and bp drops during that time. I read once, for my mother, that your body will shiver if your blood pressure drops extra low because it thinks you're dying. Is that not weird!
Another thing I didn't mention is that I take 2 full strength aspirin every day to prevent colon polyps, colon cancer recurrence and mets. ONCE in a while, if I have a headache or have strained a muscle doing yard work, I'll take a 2nd dose late afternoon or before bed. Aspirin thins your blood and thin blood makes you feel cold.