Occasionally my SUV won’t start specifically when the engine is warm. The engine turns over, then stalls, even if I push the gas pedal. If I let the car cool, it will start immediately. Dealership had car for a week but couldn’t spot the problem because it wouldn’t do it for them.
Could be a dirty throttle body. You don’t need a dealer for this, any shop can do it. Anyone remotely handy can do it. Look for a U-tube video on it.
This sounds like a heat-related ignition system failure. In the old days we’d look for a good spark coming out if the distributor and if it wasn’t there, suspect the pickup coil / ignition control module inside. Nowadays the analogous part is the crankcase position sensor - also likely to fail first when hot, and then to fail altogether.