Wow...I did not realize the car had two horns of different pitches.
My first guess is that the horn is on its way out, but not completely broken yet. But, somehow when it is hot, it still works.
I'd get to the connector where the horn is and check the voltage at the horn connector when the horn doesn't seem to be working.
There should be no voltage across the two pins on the connector when you are not pushing the horn on the steering wheel.
There should be voltage across the two pins on the connector when you are pushing the horn on the steering wheel.
If there is voltage when you are pushing the horn on the steering wheel, but the horn isn't making noise, replace the horn.
If no voltage and no sound when pushing the horn on the steering wheel, the problem is more complicated.
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