Basically, the AC system is a balanced heat exchanger which uses varying pressure to control the temperature. The high pressure side is used to transfer the heat to the outside air via the condenser. The expansion valve drops the refrigerant's pressure drastically, also dropping the temperature. The cool refrigerant then passes through the evaporator to cool the cabin, and then makes its way back to the compressor, where the refrigerant is pressurized, and the process starts again.
How sure are you that the system has the correct amount of refrigerant in it? If there is too much much refrigerant in the system, the entire system pressure rises. When the pressure rises on the low pressure side, it makes it hotter, which means it can't cool the air going into the cabin.