If so, how does it influence our sleep? And what can we do to improve the quality of sleep in regards to adjusting our body temperature?
Yes. Body temperature drops at night almost 2 degrees fahrenheit.
Cranial cooling has been showing to lead to deeper sleep and help insomniacs.
Higher body temperatures during sleep are associated with depression.
As a physician, I have a seen previous studies suggesting that taking a lukewarm shower before sleeping has been shown to help people get to sleep faster [reference needed].
Anecdotally, I have patients who report that walking around without socks on the floor until their feet feel cold also report falling asleep faster.