I lived in Oman for nine years in the seventies and eighties, so I know why you need good A/C!
You mentioned the warranty and stated that you have had the car less than two years. Isn't it still guaranteed then? if so write a polite letter to the dealer explaining what he has done and requesting that he completes the repair. If he refuses email a copy of the letter to Fiat and see what they have to say.
Failing all that there must be specialsts about who could sort out any problem, or at least determine what the problem is - no?
It really shouldn't be that difficult to fix an A/C. Is there another dealer within striking distance - Muscat maybe?