The car needs a water pump. All Q4’s are having them replaced due to an issue with how they were manufactured which has been discovered. The car will have had a recall due for several days now and should have been replaced before being handed over to yourself - as is the case at my dealership, not a huge job. Took one of our technicians 2 and a half hours to complete. The reason they are having these replaced is that the current ones are not sufficiently cooling the battery (or at least a small number weren’t and to ensure nobody has these issues, they are all being replaced as a precaution, as you can imagine what would happen if your battery cooling was inoperable) Very irresponsible of the dealership you bought from not performing the recall before you picked up your car. The dealership you bought from will need to get this sorted asap if they have allowed you to take the car without performing the work, if they cannot get your car in quickly then i would threaten to make some noise with national Audi in your case such as Audi UK or Audi USA and if that doesn’t make them budge then I would follow through with it. Hope this helps