Truly, for longevity of your ac system, you should turn off the ac before you turn off the truck anyway. The torque produced by the moving parts slamming to a stop when the engine shuts off can be very damaging to the internal components. Even if your system were functioning properly, this is a good habit to get into to ensure the continued operation of your compressor pump, etc.
Your AC continues to run even after you turn off the ignition probably because you have issues with the outdoor condensing unit. Locate your 2005 GMC Envoy XL air conditioners' circuit breakers and reset them. You may also want to check and be sure that the thermostat settings are fine.
2 years ago
Last edited at 8:22AM on 4/6/2012
Some cars run the radiator fan for a few minutes after shut down. The A/C can't "run", with the engine off. The engine turns the A/C compressor. It can make bubbling noise in the dashboard as the refrigerant continues to evaporate. The radiator fan and the interior fans should stop. If a fan "runs' change the relay for that fan, it's cheap... its on the fuse panel.