My experience and reading make me believe that the powering up and down produce more wear. I have transistor amps 25 years old I leave on all the time. I have never heard of heat being a factor in amp deterioration . I have often heard of an amp going bad from not being used. I think this is another case where theory and the real world differ. The ONLY argument I have ever heard against leaving them on is the cost of the power. In every case where I have seen this discussed the author has stated that leaving them on prolongs their life.
