One of my books suggested agitating in hot water and periodically rinsing with cold. Supposedly it helps it felt faster.
Cold water
One of the things that makes wool felt is big temperature changes, so hot wash cold rinse makes sense!
Dunking it in cold water is called “shocking” the yarn. :shock:
And it can help in the felting process. It is often not necessary. I’ve only used it as a last resort with an uncooperative yarn.