" When you get out of warm water, the contrast with the cooler air mimics how your body cools down at night."
Your temperature drops one or two degrees during sleep, so cooling down signals that it's bedtime.
I believe a good warm shower would induce sleep. Also, better a cooler room than a warmer one. I always wake up if it's too warm.
The only true wisdom is in knowing you know nothing.
I wake up if I am too cold.
I have to have it hot.
I got a heat pad and a bed buddy to comfort me.