...simply having the circuits hot and powered up in general means that they're aging. Clearly, they're NOT aging when they're off. This needs to be balanced against the thermal-cycling sort of stresses that you mention which happen during power cycling, and this is why I recommend shutting off only when you're going to be away for an extended period, such as overnight. This is, of course, most important for those components which have clear heat-related aging, but most do to some extent. Esp. vulnerable are things like electrolytic caps, for obvious reasons.