What model Jag was it, LTCAP?
My wife has a XK8, and we had to take it in a few years ago because the radiator cooling fan would run for 20-25 minutes after the car was shut off. There was also a terrific amount of heat eminating from the sides of the car, just behind the front wheels.
The car was not overheating though -- the temperature gauge was steady at 50%. (Hot to me, but she said it was like that since day 1).
Anyways, we took it to my mechanic, who worked on my older 911, and he said nothing was wrong. Note: this mechanic is no longer my 911 mechanic after this day...
We then took it to a Jag specialist, and he knew right away what was wrong. Apparently there was a defect with the water pump impeller, and all of the fins broke off of it.
Ford used a cheapo part that commonly broke.
Just thought I'd share -- it has no relevance other than being a Jag with a weird problem.

mir