I'm in the same boat-
Did a clean install, I think I picked the stock kernel (but did the install months ago so I don't honestly recall - how to check this?)
It actually has gotten worse for me over time.
Recently, I have had to carry an extra battery around with me, or I'm completely dead by 8 or 9pm even with extremely light use of my phone. On a recent work trip where I used my phone only marginally above-average, I went through three batteries, and had my phone plugged into my laptop for part of the day.
Several times I've noticed my phone is warm - today I took the cover off and specifically noticed it was warm just below the battery, but not (I don't believe) quite the antenna area which I believe is the very very bottom - if I hold my finger over the memory card slot, it's very warm.
I've also had my phone reboot randomly several times, and when I checked the dump logs it showed trouble accessing my memory card - and I'm thinking they are related - meaning, it's gotten warm, and the thermal issue is maybe causing difficulty in some way with the memory card not being able to be read, and the phone reboots.
I've installed GSAM battery monitor, because it provides a nice app-based view of battery usage, but nothing unusual really shows up near the top.
Any idea what's in this area of the phone that is getting warm, to help narrow up an app that's causing this?