I totally sympathise, our pup wakes up at least once anytime between 2am-4am, then always at 5.30am, been doing that for 8 wks, its exhausting to say the least!!!
Then I sleep with her on the couch until 7sh, as Im not willing to be up at 5.30am!!
We have tried everything, it is difficult to let her cry for long as one of our sons will go to her.
We pray she grows out of it SOON!!
Only thing I can suggest is you try a hot water bottle in the crate, you get special pet ones, they stay warm for over 12hrs.
Good luck.
Elaine