Over by the air filter's box.
intake manifold just beyond the throttle body
There're two got same name, same spec, but different shape. One on intake hose/adapter to throttle body, it's called intake air temperature sensor. Another can see through from front bumper lower section, in front of air conditioner condenser, on the bracket of power steering cooler. It's called Ambient temperature sensor. If you don't see it, it's gone, the wire or connector is quite easy corroded.
There isn't one, its wired into the ECM.
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If It is the temp. sensor and not the thermosat I believe it is the bottom of the coolant tank. I thimk you have to buy a new tank.
See this link http://www.a4mods.com/index.php?page=webcontent/pages/ECTsensor.html
Yes is in 1996
You should have gotten a letter from Audi about an extended warranty. The sensor is now covered for 10 years/100,000 miles for a falty sensor. This sensor (if malfunctioning) will cause the MIL to light up by "sensing" that the engine coolant is a couple degrees above what it should read. No Idea where it is but you shouldn't have to worry about replacing it yourself.
A bad brake sensor can cause the ESP light to stay on in an Audi. Other reasons the light stays on include a problem with the batter, loose clamp causing a leak in the intake, and worn brake pads.
its incorporated into the maf sensor.