Your car should have the motronic 1.1 fuel system with self diagnostic ability. All you have to do is turn the ignition to the ON position and not start the engine, then wait three seconds. At that time the check engine light will blick once, twice, three or four times per error found. There are 4 trouble codes with this car.
Code 1= Airflow meter
Code 2= Oxygen Sensor
Code 3= Coolant Tempurature Sensor
Code 4= Throttle Position Senser
It could be the Airflow meter or ECU in my opinion. Check the airflow meter first. The car should still run with the O2 sensor faulty.
I have a coolant sensor go out once, here is what it did: The car would start fine and run for like 30-45 seconds fine. But after that it would start to miss and run real crappy. I could not get the engine to get over 3500 rpm. This was my '85 318i. That was my expierence with fualty coolant sensors.
I got the code info from my Haynes manual. I have a 87 325 with the 1.0 motronic system so I do not have the diagnostic ability. The manual does say that the ECU has to be tested by a dealer or repair shop.
Later