Hi Raquel,
This is the question that does not have a simple answer. As one of my teachers used to say - when in doubt whether simple rules apply, consider the extreme cases. Would you keep your units on 24/7 if you only listened to them for two hours once a month? Probably not. We, therefore, can safely assume that for the multitude of applications and uses there also exist multitude of correct answers.
There are several kill mechanisms acting upon the tubes (and other components), and you correctly mentioned one of them - thermal cycling. However, there are others. Of them the cathode wear might be the most important. Needless to say, both the full operation, and the typical Standby, have the cathodes working, and therefore wearing out.
Furthermore, as is known from the reliability studies, temperature always accelerates the component failures. Its effect is exponential, and its degree varies depending upon the component's nature, but it is always there.
Also, while it is true that thermal shocks are, generally speaking, damaging, it is the rate of change that is the most critical aspect of that particular effect. There are special accelerated life tests that include high rates of temperature change, and they have been shown to be effective predictors of product reliability. However, the rate is the key element here.
By controlling the rate we can reduce the damaging effect of thermal cycling manifold - also exponentially. Therefore it is always important to understand how the product handles the changes of its state. In our particular case the tubes heat up very gradually, so the rate of temperature change is substantially reduced.
All this would of course be academic without hard experience, and that experience tells us that we do not see tubes die catastrophically after 10 or 15 years, as the rule. And damage due to thermal cycling tend to manifest itself as catastrophic failure.
What we normally see is slow deterioration of tubes, most likely due to the depletion of their cathodes. Meaning - long operating hours.
As there is no simple answer, every user has to develop his own way of operating the components - we just give him the tools. All I am trying to express here is the fact that no single universal truth exists in that regard.
Regards,
Victor