Aroc's comparison between tubes heating down and an engine heating down makes for a pretty good anology. Both have built in design tolerances, both require specific clearances / spacing for optimum operation, both are made up of a complex sum of parts that do their job individually yet sum together to form a team effort, etc...
Just like a motor, tubes run hot and certain parts run hotter than others. As the tubes heat down ( or "cool off" to normal people ), a small amount of internal shifting takes place within the tube itself. This has to do with the expansion and contraction of the metals due to thermal variances. The faster that thermal variances come into play, either heating up or heating down, the more likely severe shifting is to take place. The more internal shifting that takes place, the further the tube will be out of emmissions / tolerance and the less performance that you'll get out of it. That's because the design parameters of the tube are based on specific internal dimensions / proximity of conductors. When these dimensions & proximities change, even by a hair, it changes the performance / electrical characteristics of the tube.
This is why i suggested allowing a tube to gradually come up to operating temperature before hitting it with signal. The entire tube becomes thermally stable and levels out before stressing any of the individual components harder than others once signal is applied. While it is true that some components are under heavier stress than others inside of a tube, allowing them to warm up somewhat reduces the fatigue that they undergo. Think of it as exercising the tubes i.e. "warming up" before actually "working out". Yes, you can sweat ( build up heat ) doing both, but the stress level rises gradually.
As far as "heating down" goes, just as the tubes shifted internally from warming them up, they do the same thing as they heat down. If you get them really hot and then pull the plug on them all of a sudden, there's a bigger temperature swing to deal with as the tube cools off rapidly. Greater temperature swing in a shorter period of time causes more shifting / expansion / contraction within the tubes themselves, taking them further out of tolerance even faster. If you do this on a regular basis, your "matched tubes" won't be matched very long. Don't worry about that though, because nobody really matches tubes right anyhow : )
As you can see, warming up / heating down a tube based system, especially amplifiers where there is a lot of output and heat involved, can actually extend tube life AND provide more consistent sonics during that extended lifespan. This is something that everyone thinking about buying tube gear should be aware of before making the jump. When properly operated, tube gear IS more time consuming with more potential for degradation. This isn't to say that SS devices don't undergo similar thermal stress related problems, but it is nowhere near as severe or as rapid as it is with tubes. That's another story for a another time though kids as my fifteen minutes on Agon are up for today : ) Sean