Year 2000 bmw 316i radiator fan not working - 318 BMW Cars & Trucks

I am at a bit of a disadvantage here as I have never seen a 316 and my books and parts lists don't cover it, but here goes.
I expect that your car has only an electric fan, right? And you have already checked the fuses, right?
That fan should turn on low speed when the A/C compressor is running, or on low speed when the radiator gets to a certain temperature, or on high speed then the radiator gets really hot.
There should be a temperature sensor somewhere in one of the end-tanks on the radiator. If it has three wires, the switch is inside the sensor. The switch plug will have a ground wire and two wires that go to relays. The switch will ground one of the relay wires depending on the temperature. Grounding that wire activates a relay which turns on the fan.
With the key ON, If you unplug the sensor and ground each of the two relay wires to the ground wire in the plug (ground is usually brown on a BMW), you may be able to turn on the fan. If both speeds work, the problem is your temperature sensor. If only the high speed works, the problem is either the relay or the resistor in the fan. Most often, it is the relay. I don't know which relay it is on a 316, but the relay may click when you trigger it at the temperature sensor plug, even though it has failed. If it clicks, you can find it by the sound it makes.