Something to consider, too, is what he's eating. Some foods can cause a need for more water consumption. Also, often times chew treats that people give puppies can cause thirst, and sometimes these are the same treats that they leave in the crate to keep a dog occupied.

I'm not sure if your pup doing well in housebraking or not, you never really said. If you're not having a problem right now with housebreaking...(meaning, if the crate is dry in the morning) you could try to let him have free reign to water. I never limited my pup's water intake and he was housetrained amazingly fast.

If you offer water and then he starts having problems holding it through the night, then obviously keep picking up the water after a certain time. But if he's okay so far...let him drink, I say, and see if it becomes an issue. As you say, you're already getting up in the middle of the night anyway!

I never like restricting water unless there's a good reason for it, because dogs while dogs will eat even if they're not hungry, they generally won't drink unless they're genuinely thirsty. And I would rule out any possible medical concerns also.

Good luck, keep us posted.