Interesting. I am having almost exactly the same problem. Most of the time it works fine, but sometimes for not apparent reason, just starts blowing hot air. It feels like the compressor is kicking in, but I need to investigate that further.
Thanks for the A/C clutch relay tip. Will have to double check that, as well as the actual clutch on the compressor.
My outside air temperature display is working fine.
I did have the system leak checked and recharged which improved it's performance when working, but didn't solve the problem.
It's been intermittent for awhile, but it's starting to happen more and more often.
Completely random. Sometimes at startup, sometimes after driving for awhile.
Sometimes only for a few seconds, sometimes for a couple of days. Weird.