It could be the cars automatic choke system. When the car starts from cold the choke is in, using a bit more fuel to get the car going. When it is warm, it usually doesn't need the choke, because it is already warm enough for the car to re-start and run. Maybe the car is not producing enough spark from the plugs when warm, so its cutting out. When the choke is in it doesn't need so much spark, because there is more fuel floating around the engine. I would advise taking the car to a main dealer and ask there.
David Arnold
February 2010