A3 2.0 fsi sport air con doesn't blow cold

I have a 04 reg A3 2.0 fsi Sport with approaching 60k miles on the clock. A while ago when I started the engine, there was a weird grindy/whirry noise. When I then stopped and restarted the engine, the car was fine, but the air con was no longer blowing cold air. It blows warm air, but i'm not convinced the temperature is a reflection of what is on the digital display.
I have just had the car in the garage today (not a dealership) and they have re-gassed the system (apparently pressure was low), found no leaks and also hooked up to the fault code reader, found some faults and cleared them (they haven't explained what these were).
The upshot is, the system still isn't working as expected (they confirmed this) - ie. still doesn't blow cold air. I've looked through some of the other threads on here, and don't think this has anything to do with the ECON problem that seems to be prevalent, but happy to be told i'm wrong!

Does anyone have any ideas/advice please?

Hi Staz,
Thanks for that - I will check it out and let you know how I get on. They didn't specifically say they had retested for fault codes afterwards, nor did they say they hadn't.

It also crossed my mind that it hadn't long been in for a service and cam belt replacement when it went pear shaped - could work done in that area could have anything to do with it do you think? I also had a fan replaced (reasonably expensive job but the exact details escape me as I write this) earlier in the year as it was running on (and on) after the engine stopped.
Anyway - i'll check out per your instructions and see how I get on.

Cheers.