Over by the air filter's box.
intake manifold just beyond the throttle body
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.
on the A4's, they are typically under the front bumper cover closer to the drivers side.
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.
Need to hook upto a scanner. Check for codes.
Where is the crankshaft position sensor located on Audi 2002 Audi TT
Disconnect the wires, and unscrew the O2 sensor. You might want some wd-40 to soak up the sensor's threads before you try to remove it.
Where is the crank shaft sensor located in a Audi a6
Where is the fuse panel on a 1997 Audi A4?
not sure about an audi, but usually there are not alrm sensors on engine compartment on any vehicle , unless an extra has been installed by the owner
See this link http://www.a4mods.com/index.php?page=webcontent/pages/ECTsensor.html
I read on a diff site, that suggested there isnt one.. and that you unscrew the sensor and thread in a filling nipple.