I've heard some people mention the high pressure switch. Also have heard that their is a control switch/valve on the compressor that can go bad. I have had similar problem with random no A/C on my A3. Post if you find out what it is. Thanks
First, automotive air conditioners cannot, I repeat, canNOT, "blow hot air". They can cool, or they cannot cool. The heater can warm the air. A/C can't.
Second, for the millionth time: please, avail yourself of the car's own OBD. It works, it is a great part of the modern automobile, and DRASTICALLY speeds up any diagnostics. In this case specifically, you could already have DTCs stored for various things, including the cooling fan(s).
But on this car there is also a VERY common issue with the RCV in the compressor. And unless you can read what the refrigerant pressure sensor value is going to the Climate module, you can only guess as to its operation. And its operation (the ability to allow the compressor to make sufficient pressure) is directly tied to the cooling fans being requested on at all.