Download the Electrical Troubleshooting Manual for the 1993 318is from here
http://www.wedophones.com/Manuals/BM...g%20Manual.pdf .
According to the manual (and OEM parts listing) your car has 2 coolant temperature sensors - one connected to the temperature gauge (component B6232) and the other connected to your DME (component B6236). There is also another temp switch on the top LHS of the radiator for the thermo fan. If B6236 (front RH side of the engine, under the intake manifold) has gone bad, it may not show on your temp gauge, but can signal the DME that the engine is cold.