A couple of days ago my Pro1 started seriously overheating and draining its battery. Rebooting didn't help. After investigation I noticed it was constantly using network bandwidth both upload and download. Settings battery usage was reporting Gmail as being most greedy. Network monitoring tools were in fact showing some Google Service was responsible for that traffic.
Turning off auto-sync in Gmail fixed the issue. Battery life is now awesome with the downside that emails and personal info don't sync automatically, obviously.
I only have two accounts in Gmail, namely Google Gmail and