It sounds like the climate control unit has failed. A leak in the system (no or low refrigerant) would also cause the A/C to blow hot air, but the compressor would still be operational.
Still, do an A/C system check for leaks first to get that ruled out. I don't know of a good way to check the climate control unit, but they have been notorious for failure.
2009 ML350 (84K) - Family vehicle
2001 CLK430 Cabriolet (71K) - Wife's car
2005 BMW 645CI (124K) - My daily driver
2012 Mustang V6 (60K) - Daughter's car