I don't know much about fuel injection but if this was a carb model I would think the choke was stuck on so could it be something to do with the 5th injector?
I had a similar problem might not be the same but my fix turned out to be the air intake to the inlet manifold was not fitted correctly. Looked ok but the clamp on the large end was loose.
I might be talking rubbish here but I had a 1.6 cl had a very similar fault the car would start run for 10 miles and then lost power and cut out. But it would start shortly after and run fine. The fault was the automatic choke sticking on when running but would release after being stood for a while.
I would agree that the thermostat is faulty as after 10 mins idling the thermostat should have opened. I don't see how that affects the oil pressure light though.
