Wont start when engine is hot

the engine starts 1st time on the key when the engine is cold as soon as you have driven a few miles and turn off the engine like to fuel up or go to shop it wont restart until the engine has cooled down after about an hour in cold weather
the engine turns over and stutters like it wants to start the just dies (it seems like it has run out of petrol) once the engine has cooled down it starts again no problem????
please help!!!
the AA man said it is possably the crankshaft sensor??????????????