Audi Repair: temperature gauge fluctuates, coolant temperature sensor, engine coolant temperature sensor

Question
I drive an Audi A4 1.8T and recently noticed that the engine temperature gauge is fluctuating. What happens is that the needle will be resting exactly in the middle (where is normally is) and suddenly it will drop down to C (as if the engine was turned off) and then shoot back up to the middle again, and then drop again. Does this indicate that the gauge or wiring is faulty, or more likely a larger (and more costly) repair, such as a failing thermostat? Is there a way I can test it myself?
Anything you can tell me here is appreciated....before I bring it into Audi and pay through the nose to have it repaired :)

Thank you!

Answer
This is typical of a failing engine coolant temperature sensor, which is a common item to fail on Audi's like yours.  The replacement is covered in detail on the web forums, and is fairly inexpensive.  I cannot post pictures here, but they are in the forums such as www.audizine.com, www.audifans.com and www.audiworld.com.  Good luck,  Jan