I don't know how it is on the e30 but on the e36 there is an easy way to test the whole system without the sensor and then test the sensor separately. You could disconect the plug that goes to the sensor in the radiator and at least on the e36 there are 3 pins (one is gorund, the other two are low temperature and high temperature). With the key in the on position, when you short the ground and the low temp pins, the fan comes on at a slow speed, when you short the ground and the high temp pin, the fan comes on at a high speed.
The way I tested the sensor was: I got it out of the radiator and checked which pins were shorted (none), then I heated it up with a torch and heard a little click (at about 60 degrees celcius) after checking with a multimeter, the ground and the low temp pin were shorted. I heated it up further and at about 90 degrees celcius it clicked again and all the pins were shorted out.
I think my fan wasn't working but testing shows that it should have been. Although I did acidentaly drop the sensor and that could have gotten it unstuck.
If like mjbst111 said, you have a few friends that know electricity, you can narrow the problem down. Oh, if there are only two pins on the sensor, thats probably because there is only one temperature at which it turns on, the same precedure would work for testing it except there is no high temp pin.