Harmonics in an audio signal are high frequencies.
Sometimes the volume control of an amplifier is turned up too high which causes the output to reach its maximum voltage swing which causes clipping which creates many harmonics. Then the tweeter is overloaded with harmonics which can burn it.
Harmonics at the input of an amplifier do not cause it to burn if its heatsinks are big enough for normal saounds and its load impedance is not too low.
The maximum heating occurs in an amplifier when its output power is about 67% of its power at clipping.
When it clips more then its heating becomes a little less because then the output transistors are not linear, they simply switch on and off.