This is a know problem on these SUVs and there should be a TSB floating around on it.
There are three possibilities: The motor, the controller (these use controllers rather than resistors) or the wiring at the connector. The TSB is directed at the melting wires/connector at the controller. To access all of it, you need to remove the cover under the dash on the passenger side. One of the screws will be very difficult to remove and is usually not reinstalled by techs. I think it is in the back corner nearest to the firewall and the center console. It doesn't have to be removed to access the controller and the fan.
Once you get that cover loose enough to access everything, check the wires for any that look melted. If there are any, then you have your problem. If they look fine, start your Yukon and turn the fan on to a setting. Then start moving the wires around to see if the fan responds. If it works, then you can replace the plug yourself or take it to a dealer. If it is still no good, then you are looking at either the controller or the fan. I was told to just replace both when I had this issue. I think parts were like $120 or $130 on Amazon. The controller is the cheaper of the two, so you could try that first.
