On my 1520/RM-938, I initially had "so hot I could barely touch it" drain. So, I disabled all but the bare minimum background tasks and rebooted. Since then, it's been running fine; maybe a little higher battery drain than before, but nothing to write home about.
On my 1520/RM-940, I just let the stupid thing cook itself on the charger overnight. It ran all day yesterday and so far today cool to the touch with about the same discharge rate as the RM-938.
I was thinking that maybe it's just Cortana growing pains or something.
I did notice in GDR2, on my Lumia 925, that often, Visual Voice Mail would drain the battery in about an hour (with expected overheating behavior), so I've been in the habit of leaving VVM turned off ever since. I don't know if it's still an issue, but frankly, I don't want to find out. No one ever calls me anyway, so I have little use for voice mail.