My 2002 Civic a/c will go on initially when the car is cold and will blow cold air nicely. Within a few minutes, and it seems related to the rpms, it switches to blowing hot air. After that it will not blow cold air again until the car has completely cooled down. Predictably did this all last summer. Suggestions on diagnosing? Could it be a fuse or relay?

 

Usually this is the compressor clutch gap. When the coil gets hot its magnetic force drops, to the point that it can't pull the clutch plate in. If that's what it is, it is simple to remedy by removing the clutch plate and taking some of the shim washers off of the shaft.

Check that the compressor wire is getting power when you press the button and it's supposed to be running. When the A/C is supposed to engage, the radiator fans will come on immediately regardless of the engine temperature. The fans starting and stopping with the A/C button means that most of the controls (except possibly the compressor relay) are OK. Compressor relay can be ruled out by swapping it with the defogger relay in the same box, it's the same kind of relay.