Does the temp. Sensor on a '01 elantra perform a function other than working the temp. Gauge, and turning the fan off,and on?

This problem seems like a missing ground, but that somehow doesn't seem likely. The temperature sensor screws directly into the water jacket of the engine (which is a good ground).

If, somehow, the fan ground is not working (it is not connected to ground), it is possible that the fan will establish it's ground from anything else that it's ground wire is connected to. That means that when something activates (such as a temperature light), it could cause the fan to turn (but not at full speed).

So, check the ground of the fan and make sure that it is connected to the battery ground.

Hi No not usually that is it's sole purpose however be warned it could be in a chain of other sensors linked in series as most sensors are these days each being poled by the engine management system as it reads them it requests information.so you simple can not remove them.