When the issue started I had the throttle body, IAC & MAF cleaned and new filters installed. That didn’t resolve the issue. Next was a deep AUTEL software scan listing about 5 pages of blind fault codes. I was advised this was the PCM. I sent the DENSO PCM out to a module rebuild company. I received the module back after repair, reinstalled it and still have idle stall after heat soak. The car is a 2007 XK-R coupe with 65,725 miles. Module is Denso V8SC 7W8314C568BA
Sounds like a pretty complex problem to figure out. Without doing a lot of scan tool work, its hard to narrow down the culprits, but I’ll mention that I have seen coolant temp sensors cause some crazy issues over the years including endless fault codes and poor driveability. It may be worth replacing just to eliminate it as a possibility.
I had the PCM rebuilt for $250 and finally got a code for the MAP (manifold absolute pressure sensor). I ordered a new MAP sensor before pulling the old one. MAP sensor approximately $80, replaced the gummed up original and now she runs like a champ. It idles at a fairly low RPM with no issues.
I have owned a number of Jaguars and have found that if you are patient about locating the problem, they are relatively inexpensive and easy to repair. The PCM was a bit of a pain to pull out due to the wiring harness connectors which are easily broken if you are uninformed and impatient. It took 2 days of lubrication and slowly rocking the locking tabs to remove them.