Well it's a hot soak problem of some kind. If you doubt that then next time it is fully warmed up, park it with the hood up. When you go to start it it will start fine because the heat didn't build up. That will prove it is hot soak. As far as the other symptoms it does sound like the boiling fuel problem that was stated previously. My Supra had the same problem. Basically there was a window between 20 min and 40 min when it would be hard to start. Luckily I usually was parked either less or more than that, or not fully warmed up. I would think other people with the same car would report the same symptom though.

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1998 C230 330,000 miles (currently dead of second failed EIS, yours will fail too, turning you into the dealer's personal human cash machine)
1988 F150 144,000 miles (leaks all the colors of the rainbow)
Previous stars: 1981 Brava 210,000 miles, 1978 128 150,000 miles, 1977 B200 Van 175,000 miles, 1972 Vega (great, if rusty, car), 1972 Celica, 1986.5 Supra