Civic A/C

My daughter has a 2001 Civic and is experiencing problems with the A/C. It works fine when the engine is cold, but quits completely when it warms up. The dealer that she bought it from says it needs a new A/C compressor and two other parts. I doubt their diagnosis because it works when the motor is cold. If the condenser works at all it can't be bad. Does anyone know whats wrong? I've heard that this may be a common problem.