I put a dog safe soft toy in the crate around same size as the puppy as it gives them something to snuggle with.
Not had a peep right from the first night from our new pup at 8 weeks. He has a small enclosed crate with vet bed in the bottom. Last trip out at about 23:00 wakes around 6:00. Only had one wet bed in 11 days on the second morning and that was my fault as I didn't hear him wake and cry to go out. No drinks overnight, but we have air con running as needed. House training coming along nicely now as he is starting to go to the door and ask to go out.
He is a jack russel of uncertain heritage, otherwise known as a "wee brown dog"