Hi, possibly one of the commonest causes for this sort of behaviour is the fuel pump relay (103 under Fuse box cover). This can give a variety of symptoms, most not logging any fault code, but it is a simple and cheap item to try first. Also have a look at the throttle body, after a fair few miles without cleaning it can get a build-up of oil residue and cause poor idling. Next on the list would possibly be the cam position sensor, but this should log fault codes if it fails. Then we get into areas such as engine temp sensor (faulty readings from this will give incorrect fuelling and engine cut), bad earth on coil pack (another known area of running problems), Tired Idle Control Valve, plugs, leads, rotor arm, dizzy cap. As the car starts again after cooling slightly, it would seem to indicate a heat soak related problem, so I would look at 1. Fuel relay 2. Engine temp sensor 3. Cam sensor. Hope this gives you something to go on.