Falling asleep is closely tied to a drop in core body temperature. Once that is clear, several unrelated-sounding pieces of sleep advice turn out to be the same piece of advice.
Core temperature runs on a daily cycle
Body temperature is not fixed. It rises through the day, peaks in the early evening, then falls across the night to a low point in the early hours.
The fall begins shortly before habitual sleep time and is driven by the same internal clock that governs alertness.
Sleep onset clusters around the steepest part of that decline, which is why the evening hours just before it are often the hardest time to fall asleep.
Heat leaves through the extremities
The body lowers its core temperature by opening blood vessels in the hands, feet and face, moving warm blood to the surface where heat escapes.
This is why hands and feet become noticeably warm as a person gets sleepy, while the core is cooling.
Cold extremities restrict that flow, which is the mechanism behind the observation that cold feet delay sleep onset while warm socks can shorten it.
A warm bath cools you down
Bathing before bed appears to contradict the pattern until the sequence is followed through.
Warming the skin triggers vessel dilation at the surface, and once out of the water that dilation continues, accelerating heat loss and dropping the core faster than it would have fallen on its own.
The timing matters more than the temperature, since the effect depends on the rebound rather than on being warm at bedtime.
Room temperature works on the same variable
A cool bedroom assists the same process by widening the gradient between skin and air, allowing heat to leave more readily.
Bedding complicates this, because a heavily insulated bed can trap the heat the body is trying to shed while the room itself is cool.
Which is why people often sleep better with a cool room and a warm cover than with a warm room and light bedding, despite the two feeling similar at the moment of getting in.
Why late exercise and heavy meals interfere
Vigorous activity raises core temperature and keeps it elevated for a period afterwards, working against the evening decline.
Digestion produces heat as well, which is one contributor to the difficulty many people report after a large late meal.
Neither is a universal rule, since individual variation is wide and some people sleep perfectly well after evening training, but both act on the same underlying variable rather than on separate ones.