Why does my 2011 gmc terrain blow hot air into my cab during driving

Blend Door Actuator issue which is a servo operated door that closes off the heat and direct the cold air instead. It is a known issue on them. See the videos.

https://www.google.com/search?q=2011+gmc+acadia+blowing+hot+air+on+driver+side

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Compressor clutch not engaging Ricks Free Auto Repair Advice

StabiliTrak Problems - Free Lemon Law Help

www.lemonlaw.com/wordpress/stabilitrak-problems/
Oct 22, 2012 - Having StabiliTrak problems with your GMC, Buick, Chevrolet or Cadillac? Get free ... We owned a 2011 gmc Terrain with same issues. ... #8 Bill Hale says: ... A warning came on saying that I needed my Stability Serviced.

You paid for it, take it back. Don't let them get away from not fixing your truck.

It isn't enough for the thermostat to work but also to verify both the heater (water) flow and return is getting virtually as hot as the top radiator hose as systems can airlock and sometimes other things can happen.

The heater matrix is unlikely to be blocked or coated considering the age so if plenty of heat is potentially available the reason it isn't emerging in the car is likely to be a matter of control - jammed flaps, disconnected linkages, faulty electric or vacuum servos, electric or vacuum supply interrupted or defective control circuitry.

check blend door and heat actuator

There could be several reasons for this.
The internal heat is generated from the engine coolant system and is controlled via an control mechanism which you activate by adjusting the internal heat settings.
This control could be faulty, the air circulation fan inside your cab could be faulty or it could be a simple blown fuse.
In many cases where a leaking heater system could cause engine overheating a lazy mechanic would bypass the heater function and restrict the engine coolant from circulating through the heater coils.

My suggestion is to check all the above and you should have the problem sorted, good luck.

if your radiator is not full of anti freeze (water) their is nothing to flow through heater core to make heater work.

Most likely is the Thermostat that you would need to change .

You have a plugged heater core.