Hmmm...something like this has happened to me twice, only in reverse.
The outside air temperature reached 102F and the CD stopped working. The
radio worked OK, but nothing happened when you press the CD button. When
the car cooled off after running the A/C for a while, the CD started working
again. This was in El Paso, Tx.
The second time, I was in Phoenix. The OAT reached 109F and the CD stopped
working after the car set unattended for a while. It returned to normal after
we ran the A/C on high for a bit.
I will try the trouble shooting method Mazdadude mentioned when everything is
working correctly, then when the CD stops. It might narrow down the cause.
Thanks, Mazdadude!