One point of clarification, please. When you say “The vehicle heats up quickly (if) running down the road” do you mean the cabin of the vehicle or the engine temp as read by the gauge? If the latter, one thing you didn’t mention was the thermistor controlled fan clutch-- if the fan’s going full-speed, it can stop your motor from warming up until you start driving around.
The vacuum theory’s a possiblilty, although in my experiance, you get the opposite effect from a vacuum leak-- heat at idle, but not when you open the throttle. I haven’t had the issue with later-model GM products though, so perhaps they’re designed that way.