Woolfy:
Welcome to the forum
. You will find lot's of helpful folks and information here.
This is my opinion only but unless a class A is very small, I would suggest you look for one with two roof AC's. A lot of heat comes in via the large windshield of most class A rigs. We had a 32' 1997 Winnebago Adventurer before the current rig with two roof airs. We had no problem keeping the rig cool running the generator while underway.
Newer Winnebagos (above the most entry level rigs) have the basement air conditioners/heat pumps which seem to do a good job.
With our current rig, unless it is very hot (mid 90's and up), we keep the front of the rig very comfortable running the dash air. You are correct, that puts additional load on the engine but we've had no problems.
Whichever you choose, a fan or fans moving air in the rig will also help move the cool air around.