I don't know. But yes, that piece of wisdom has been passed down through the ages, and many people still reach for the carton of milk when they have trouble drifting off to sleep. Sipping a cup of warm milk after everyone else has gone to bed is comforting, but whether it can help you get to sleep faster remains unproven.
Warm milk makes you sleepy because of a chemical that becomes active once the milk is heated. The chemical is called Tryptophan. It is the same ingredient that makes everyone sleepy after eating turkey at Thanksgiving dinner. Also the warmth of the milk raises your body temperature and is often enough to trigger the slowdown response just like on warm days