Did you turn off "powernap" in settings? By default, a mac would wake up to download mail, run backups, and do other things in the middle of the night.

Yeah, that's with powernap off.

I've experienced this with Mac laptops that I've got loads of stuff running on, but not on stock configurations, so I suspect it's some piece of software rudely waking it up every so often for its own inscrutable reasons.