If you reset the SMC then the Energy Saver settings should be back to their defaults. N10248 makes a very valid point that it could be an oversensitive mouse or keyboard so maybe unplug or disconnect these overnight to see if it still wakes up. What other peripherals do you have plugged in or connected?
I've had my iMac do the same thing, probably about 5 times since I got it in February. I don't think it's happened since I last reinstalled the OS, however since it's starting from off I think that could just be a coincidence (or does the installer reset the SMC?)