My 2002 audi a3 1.9 tdi is overheating? I have

The radiator fan is of no value above 35 mph due to the amount of air being forced through the radiator. Your problem appears to be with the thermostat. It's relatively inexpensive and easy to change. You should have the fan repaired for low speed and idle cooling.. It's more than likely a faulty relay, It is also a quick fix and relays are inexpensive. Good Luck, Ned

If your cooling fan is not working you solved your own problem. The cooling fan is what helps your radiator perform its function. The radiator cools down the antifreeze mixture by separating it into small tubes separated by air fins, the fins allow a greater surface area for air. The radiators main function is to dissipate heat into the surrounding atmosphere which it can do well at highway speeds without a fan, but most modern cars need a cooling fan to help pull air across the radiator.
The wiring diagram for your vehicle suggests that there is a 5 amp fuse 4 and a 40 amp fuse 42 that run the radiator fan and control which should be located in an under hood fuse/relay box. Check them with a test light on both sides, with the light to ground you should see a positive voltage at both sides. the 40 amp would most likely be a maxi fuse, or a larger size then the regular atm fuse for the 5 amp,

Are you sure it is an 02 A3?
have you had any work done that could have affected the cooling system?
The system required evacuation and the fluid must be forced back into the system to eliminate air. I would hook it up and evac. check the hoses for compression and then recharge the coolant. with out a fan the system will overhear, check the relay.