Bah, hint taken...
No error codes stored in the ECU?
Definitely sounds like heat soak, but not in the traditional sense. It sounds like you have a component which is failing as the engine bay warms up. The first thing to do is to test the coils, fuel pump resister and relay, injector resistor pack and AFM RIGHT AWAY once the engine dies or starts messing up... You won't have a lot of time to work on it so try to be quick, but thorough. Once you reduce the number of possibilities you can use a strong hair dryer or heat gun to bring the parts up to temp to continue testing until one fails. The last time I had this happen the AFM was the problem (no error codes were stored though).
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