Stalls and will not start when hot

This car starts well and drives brilliant for the first fifteen to twenty minutes. Then it stalls and shuts off if you are driving or if it is idling.

If you parked somewhere it does not want to start. It turns over and just as it wants to start, it backfires (too much fuel probably).
Tried once to start it after it was parked at a shopping center quite a few times in a row until the battery was flat. It just backfired every single time as per above explanation.

And every time after an hour as soon as it has cooled down or so it starts up easy again and drive perfectly as per above.

We checked the spark in the spark plugs when it would not want to start and there were spark on all three spark plugs. I do not know if enough though.