Had this XJl for about for few months. It over heated but still drives. The only issue is the idle it will start but rpms will eventually start jumping all over the place and stall. If driving or reving the engine runs and sounds fine. Does this sound like the engine is done for or a sensor or fuel or air problem?

 

This could go so many different directions. Is there air in the coolant suggesting a blown head gasket? Have the PCV diaphragms been renewed? Hunting or uuneven idle symptoms can suggest a vacuum leak. Are there any check engine lights or codes in SDD that suggest a stretched timing chain? That can also cause idle problems especially when warm.

 

Don't guess. Get the Diagnostic Trouble Codes. Any unusual engine noises or odors (antifreeze) when you open the hood?