You've been mislead somehow.
It's 4G LTE, not just 4G. There is no such thing as 4G except in marketing terms. The correct nomenclature for the high speed service for both AT&T & Verizon is 4G LTE.
If the phone is very warm, that is another problem.
I have four different 4G LTE phones on two platforms & two carriers. None of them runs warm. They all stay cool to the touch.
You've been mislead as well.
The exact reason he put "4G" in quotes in the first place is because of what you are describing so pedantically.
He is talking about the HSPA+ network that AT&T and, when connected, the iPhone call 4G. He is saying that when he is connected to HSPA+ ("4G") his battery drains faster and his phone is warmer, as opposed to when using LTE (or as you so insistently put it, "4G LTE").