Lovely time of the year to get this problem.
Got an A3 pre-facelift with climate control, the air-con was working beautifully this morning, but put it on later, and it didn't cool the air... asr3.
The only thing I did in the meantime was run the engine, stationary, with me in the car, air-con on for about 10 mins - worked fine then.
Next time I get in the car - no cooling.
Answers on a postcard to the address below....