Generally speaking, it's not heat per se that hurts components, but rather the hot/cold cycles that occur when they are turned on and off. Everything expands or contracts in response to heat or cold, and the repeated expansion/contraction that occurs when components are turned on and off wears down components over time.
Thus, not only do components sound better when left on 24/7, they are much less likely to break (it's counterintuitive, but true).
Thus, not only do components sound better when left on 24/7, they are much less likely to break (it's counterintuitive, but true).