Hot baths are used by various people with insomnia to assist with sleep, in particular people who have complains of insomnia and difficulty falling asleep. The idea is that you heat core body temperature up a little bit before bedtime which then, when you get out of the bath, leads to a kind of relatively more-rapid decline in body temperature, which is thought to then assist with sleep-onset. There have been studies showing that this has been effective, particularly in older insomniacs.
I know of no formal, controlled studies - although there may be some - that look at cold baths as a way to initiate sleep. We should be aware that most of the studies on heating and cooling have been done on people with insomnia, rather than in normal sleepers. Most people fall asleep within 15 minutes or so anyway, and it's not clear that you need to modify anything within that range to begin with.