The Thirst would set in at nightfall at 19:40pm (as of Alpha 4), during which the player had to drink from the well by the hideout in order to survive and not die from The Sickness.
The thirst was removed along with the Well in Alpha 6.0. While the well has been re-added as a prop of smaller importance, the Thirst remains out of the game.
The well now allows you to heal up once a day.