If the engine is hot, it needs to be checked for a cooling system issue. Thermostat? Cooling fan issue? Other concern? Testing is needed.
If your engine runs too hot, your air conditioning system will indeed shut off until it cools down enough.
RepairPal Certified shops can diagnose and repair your 2009 GMC Yukon. They provide transparent pricing with a minimum 12-month or 12,000-mile warranty on repairs and services.