'88 5kCSTQ Temp. Sensor problem?

[wenode@perelandra.cms.udel.edu (Vinod Arekar)]

88 5kCSTQ 95k miles
The temperature sensor is playing games!
I've had the temp needle stay within half most of the time.
On Monday I was in a bad stop-go-stop-go traffic, and the temp
needle went to close to 3/4th (I have two bandwidth_indicating dots
under the "cold" line and under the "3/4th" line on the gauge,
indicating that beyond 3/4th is where one should worry... isnt that 
what it's supposed to mean?). When this happened, the temp. warning light
came on, along with beeps. After hitting the interstate and getting 
away from the stop-go, when the temp gauge needle settled below 1/2,
the warning disappeared.

Same thing happened on Tuesday. In fact, the warning came on even before
compared to on Monday. On both these days, if I press the "Check" button
for the cyclic checkup (before ignition), the temp check would report
failure. Does this mean that the temp sensor is faulty? What exactly
does this "Check" do? Does it check if sensors are OK?
Here's the interesting part... Today (Wednesday), I had stop-go traffic
near a toll booth, and the temp needle went close to 3/4th, and after
I returned to normal interstate speed, the needle came below 1/2.
But the temp warning did not come on!! I pressed "Check" and the
cyclic checkup did not report any failures.

This is my first Audi (def. not the last one!) and I don't know 
if temp needle rising so much (almost a quarter) is normal.
This is not the norm in my other car (Mazda 626). Also, I'm a little
puzzled about the temp. sensor.
Another of my puzzles -- the ABS OFF light coming on suddenly -- 
has become background worry now. I havent had that happen since
monday... pleasant surprise.

Thanks in advance,

Vinod