You would have to be over-driving the amp for one hell of a longtime before if
would go into melt down even if there was no thermo protection which most amps
have anyways. If anything would hurt the amp would be the speaker that would
get damaged in the process, but that's not the question at hand.

Care to explain how this can hurt your amp ?

Overdriving an amp can be harmful due to excess heat. Most amps hold up
reasonably well though.