Weird. I had a T-Bird that did the same thing. It was a 1980, and it was vapor locking. Not really a possibility with fuel injection, though.
Are you getting any engine codes? I know that the ECM monitors engine temp and makes adjustments based on that, and other factors. It sounds to me like a sensor somewhere is giving the computer a screwy number once it's warmed up, that the computer can't live with. Or perhaps the computer itself isn't doing it's job once it gets the higher temp numbers.
Have you checked to see if anyone makes a 4-barrel Holly conversion for the 1MZ? You could eliminate the computer altogether. That would solve a whole host of problems.
Ok, seriously though. It sounds like computer/sensor stuff to me. It might be worth the 50 dollars you'll get charged to have a dealership hook it up to their extra-fancy computer and diagnose the problem for you, then take it home and do the repair yourself. As I understand it, the dealers have access to software that can get more info from the cars computer than you can get with a simple code reader. I've used this approach with a lot of success in the past.
Good Luck!