Factory reset seems to have worked for me. Battery life has been back to normal today. Phone is cool to the touch and seems to be performing fine. I did an LG backup before the reset, but I ended up letting Google restore everything instead. I'll likely delete that at some point. I'm still on Android 5.0.1 so nothing seems to have changed there, but clearly there was an issue somewhere.
The reset wasn't as bad as I thought it would be thanks to Google having most everything backed up. It brought back my apps (which wasn't a huge deal), but you will still have reconfigure all of your home pages as they are all just in the generic Apps folder (save for a few of the LG, AT&T, and Google apps). Thankfully most apps are in the cloud, so a simple login gets you back to where you were. I will have to manually add my non-gmail email addresses back, but that's no big deal. Phone settings seemed to be mostly reset as well. I think the G3 separated Videos and Screenshots into their own folders and I'm not 100% sure Google backs them up by default. Make sure you double check that in case it matters. The process was quicker than expected as well. Google installs all the apps in the background while you are free to use the phone.
Thanks!