If the phone screen is on and you're quick charging at the same time, there will be quite a bit of heat. I'd just let the phone do what it wants to do in this regard. Heat is never a good thing for electronics in general, and particularly electrolytic capacitors and batteries, too. I would not root to get faster charging while the screen is on.
My N8 charges very quickly using wireless chargers (that I have modified so the phone sits in the sweet spot when in portrait orientation and with a clunky case installed) both with and without the screen on. Fast enough for me, anyhow.
I was watching DirecTV on the phone while the phone was on one such modified wireless charger last night, and it charged from about 50% to full in an hour or so. I can't complain about that.
I wasn't measuring the time carefully, so don't quote me on an exact figure, but suffice it to say that I was happy with the charging speed while running the screen.