On my Sierra and My friend's Envoy XUV the same thing has occurred. You have to go to the dealer and get a new blower resistor. It is located at the feet of the passenger side of the vehicle.
There are 2 harnesses and 2 bolts to change the part out, it takes all of 10 minutes with a socket set to change this part out. At the GMC dealer it costs ~$80. They have completely redesigned the part...sounds like it should have been a recall.
I have found with mine that the heat on my truck is now significantly slower and cooler than previously and the engine temperature gauge bounces around alot more now. I'm not sure if they are 100% related but it happened at the same time.