You should vote up the feature requests to start a new ride without quitting the game. That would seem to be to be a better overall fit than one specifically about cooling down separately.
e.g.
In a race or group ride, the game already allows you to cool down separately in many cases, I think. If you warm up on Watopia, then transfer to London for a race for example, after the race it’ll ask if you want to go back to Watopia or stay in London to continue riding.