the thermostat is located behind the waterpump, its kind of a big job to do. if you can find someone to do it, try to find a failsafe thermostat. A failsafe thermo is a thermstat that if it goes bad it will go bad in the open postion. its about a 1000 dollar job, so if there is a problem again, at least you can still drive the car.
The thermostat on a 1998 2.4 Audi a6 is located on the radiator under the top hose assembly. To access it, you will have to partially drain the radiator.
If this is a 2.8 V6 the thermostat is located on the front of the engine. Ask 'Where is the thermostat located on a 1995 Audi A6?' on this site and you'll find someone has done a great job of explaining how to find and replace the thermostat.
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You have to take off the front end of the engine, as if you were replacing the timing belt and water pump, huge effort for a thermostat.
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It is under the back seat.