1998 Jaguar XK8 hot restart

1998 Jaguar XK8 V8 Automatic 125000 miles

I had the transmission rebuilt then noticed a restart problems when engine is hot. This was a everday problem. Back to shop and tech's had no luck. Got them to replace starter. Problem went away few weeks, twice in two months. Each time I would open hood and wait 10 or minutes and restart right up. Recently problem occurs after a long run 20 to 30. Minutes on every restart. Gave to machanic and he thought maybe throttle body at first. He got jag software but still could not pinpoint. Said could be relay on sensor? I swap out ignition relay with horn, didn't fix. So back to square one. Won't restart when hot until I give it time to cool down. Jag bullitin # 30339 might be related. Any help appriciated. Walt van court