Yes, it could be the FM tuner--maybe a component in the FM tuner section is heating up and failing when it gets warm.
I doubt it's the audio amplifier, why would the problem not happen on AM and when playing the CD if it were a problem with the audio amplifier?
To diagnose a problem where a component fails when it gets warm, professional technicians will use "freeze spray" to chill the various components until the problem goes away, at which point the likely culprit is the last component that got freeze spray applied.
Does the problem seem to be temperature dependent at all?
