Severe power loss extreme hot weather

I drove my 2003 XG350 in 100+ degree weather for over 500 miles. In Reno, coming off an off ramp, there was no power to accelerate. I thought I ran out of gas, so I pulled over in the shade of the overpass.
10 minutes later I started the car and it ran fine for another 250 miles.

This happened again the following day, after driving about 200 miles, after a period of 3-4 hours driving at highway speed, then about 10 minutes of stop/go idling in 100+ weather.

Anybody know what might be going on? The power loss is strange. The second time it happened, I found that it will eventually accelerate to speed, but very slowly, and only if I'm really gentle on the accelerator. If I depress it too sharply, it cuts off completely as if it is about to kill the engine. Very strange. So I limped to a gas station, parked in the shade, waited 10 minutes, and I was good to go.

Power loss is usually associated with fuel delivery issue or catalytic converter restriction/collapse. Hot weather (only) points more to the fuel deliv. problem. boiling fuel could be one of them, (fuel pump) pressurization=heat gain + external heat? Of course, it could be the exact opposite, fuel pressure reduction due to inefficient or insufficient pumping.