My 9+ week old puppy is crated at nights.  She was understandably a little upset the first night but settled down quite well after that.  She has been waking me up around 5am - which is ok as i'm up early anyway.  For the past few days it's been getting earlier and earlier - 12.30 this morning!!  She is now barking quite loudly so very hard just to let her get on with it. 
I have sometimes put her in the crate during the day after meals to 'chill out' without the others and she's fine then.
Any ideas about how to keep her quiet at night?

Crate training can be really hard when this happens. There is lots you can do to make her crate a bit of a safe haven for her (as opposed to a prison).
Feed her her meals in there, so she starts to associate it with treats.
Never put her in there as a punishment...
Pop her in there whenever she goes to sleep in the daytime and leave the door open.

You can think about moving the crate closer to you if needs be. A friend has a young pup at the moment and after 2 nights of broken sleep moved the crate to outside their bedroom...bingo. Sleep.

I could never just leave pups to cry it out, I never could do it with my son either...I would have ended up grey and with ulcers! I also have neighbours....
I would leave the radio on a talking channel (although coverage of the war on Radio 4 was not suitable listening for pups so young...). If they woke I would come down, let them out, then turn out the light (crate was in the kitchen) and sit at the side of the crate until they nodded off,even stroking them through it once they were lying down. I would then sneak out once they had settled. Initially this takes forever (or feels like it) and I have been known to nod off on a cold kitchen floor...but it's worth it in the long run!) Gradually it takes less and less time. They need to know that middle of the night is NOT playtime and cuddle time...it's sleep time.

I also try to teach them to settle early on (not that you can tell with my muppet these days).
When the pups were lying down and sleepy (not sleeping) I would reward them with a calm tickle or treat (nothing too scrummy). We often don't praise them when they are actually doing exactly what we want.

You can also try putting a cover over the crate,a light one in this heat...the light may be disturbing her. I know one of my pups would only sleep with a cover over their crate (and he was a winter pup).

Make the crate a 'happy' place...and hopefully pup will soon get the idea. I have had a couple of pups though that hated their crates.