I've had both of these issues. The first one (heat) I noticed because the phone was sometimes being held 100% awake whenever I plugged it in. Check out your battery graph to see if the same thing is happening?
The second I noticed was that the phone either would not charge, or would charge very slowly on my Ventev 2A charger. However, when I switched back to the OnePlus charger it would work fine.
Honestly, I think they must have cut a buttload of corners on the hardware of this phone - there are so many quirks and oddities... that's 'Designed in China' for you, I guess.
Re. the problems from my previous post... I've switched to the latest PA 5.1 release, and the phone is much more usable, though GPS still seemed a little wonky yesterday.
I really like the idea of the OPO, but can't wait to move off it on to better hardware... probably Sony next, if they're still around!
Su