2011 Denali. And its warm outside. So air is in even tho it's "not on"?
I'm not super familiar with the 2011+ trucks, but yeah, GM likes to run the A/C to dry the air, then heat it back up to your desired temperature with the heater. Makes for a more comfortable/consistent interior.
However, it shouldn't noticeably change temperature when you switch between inside and outside air, as it knows which place the air is coming from, and the temperature of each source, so it should be able to add the right amount of heat to keep the air out the vents the same. My 2003 does that without issue.
If you've hit the A/C button to turn the A/C off, and the compressor is still cycling, then something is not right. The truck is supposed to let you override things as you see fit. Might be time for a trip to a mechanic in that case.