I see that a lot of others have talked about this issue. I received the 6.0.1 update last week. Since then, my phone has been running warm and the battery life has been abysmal. Checking the battery by running app does no good. However, see the attached battery graph - the phone never really gets to sleep. Some of the forums talk about a wake lock. I can't diagnose this since I have no desire to root my phone.
Some who have - seem to think its an OS problem. I wish they'd hurry up and figure it out.... This is a problem.
The most recent postings on this forum seem several months old. Anyone have any newer insights?