When you first turn on the A/C, go outside and see if the low speed fan is coming on. If it isn't, the compressor will shut off after a bit. Once you are moving, you get airflow, and all is cool (so to speak). I am guessing that once you have warmed up a bit, the high speed fan is coming on at the stop lights to take care of engine cooling, so you never know for sure if the low speed ever came on in the first place.
Anyway... Check to see if the quieter of the two fans comes on when you turn on the A/C. If it doesn't you will want to check the relay, and if its ok, then check out the rheostat down by the ignition coils. (Its the little metal box with metal springs inside) Mine happen to have a corroded connection there...repairing it helped me keep my cool (so to speak).

Hope this helps...

-Larry

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It is a truism that almost any sect, cult, or religion will legislate its creed into law if it acquires the political power to do so. Robert A. Heinlein


09 Jetta TDI
1985 300D