Hey, I've had a Jag and a Supra (unfortunately only the normally aspirated 3.0i) too but I had the Supra first and then the Jag. Anyway to your problem; I don't think it's reduced fuel flow due to a dirty filter or such like as I imagine it would idle ok. If there's enough fuel flow to get you through a short journey there would be enough to enable it to idle. Things that spring to mind are:

(1) Engine partially seizing.
This is quite possible if it's ok again once it has cooled down. My Supra went through 2 sets of big end bearings while I had it (about a year). Mine didn't seize it just got knocky. I also know that the previous owner had the big end shells replaced too. The Supras do not have the reliability record of other Toyotas. Supra big ends are not easy to replace either 'cause you can't just drop the sump. You have to take the whole soddin' engine out. I'm not suggesting it's the big ends, that's just a for instance.

(2) Ignition timing going adrift.
If something in the engine management system is overheating then it might cause this but I don't think it's likely to be honest.

There are probably many other things that it could be. Modern cars are so complex. Maybe something else is seizing and putting undue load on the engine. Basically check everything you can. Is it an Automatic? If so maybe that's playing up. I don't think anyone can give you a definite "it's this" without looking at it. I hope you find out what it is and it isn't serious. Let us know how you get on.