The band got very hot earlier, was just browsing while charging, not the back of the phone thou, that was just a bit warm.I'm not watching videos, gaming or anything major -- seems to run hotter than I remember of the 4S. For example, I'm syncing right now and the phone is noticeably warm.
Speaking of battery, its great on the iPhone5, nothing like what we saw when we got the 4S. On standby I saw no drop in percentage and I got 6 1/2 on a full change yesterday.I haven't noticed an increase warmth with normal usage, but I did notice it warmer when syncing like yourself.
It was nothing uncomfortable so I doubt it will have an affect on the battery and since it's only happening when I sync or charge I don't mind it.