Is your other dog crate trained and in there at night too?
Are they near each other?
I had this problem when I got my new puppy last week.
I had my new puppy in my room and my other dog in the hall.
They both cried and cried.
But once I figured that I would put them both in the hall they were fine.
Also how long have you had your puppy? You shouldnt start to crate train them until you have had them for a week or so.
Hope this helps!