I'll only add that some gear, such as high bias AB or Class A amps will pull considerable power all the time, even at idle. This means that they have to be able to dissipate heat. Since they do tend to run hot, these devices tend to show the most marked difference between "cold" and "fully warmed up". This probably has to do with the fact that they have the greatest temperature swing from not being powered up to normal operating temp. Switching or digital amps tend to show little difference in my experience since their temperature variations are not very much at all.
As far as digital goes, how it sounds cold and "hot" will vary depending on the stability of the circuitry used. Most "decent" digital gear will obtain excellent stability within 4 hours of being powered up. Some designs, being slightly more stable than those mentioned above, will come up to operating temperature faster than that.
As a side note, my $18K Military Spec signal generator is not worth "mud" until it has been on for about 2 hours. According to the manufacturer, it should achieve total stability within 15 - 20 minutes of turn on. On the other hand, the sig gen that my business partner uses ( same model but lacking higher grade Mil Spec parts and cost about $3K less ) seems to be just fine after about 15 - 20 minutes. Both units easily meet spec and were recently calibrated, but it just goes to show that there is obviously a difference due to parts tolerance.
The bottom line is that you have to try them and see what works best for you. Personally, if i was going to conduct such a test, i would leave the system powered up for at least 48 hours and preferably 72 hours and then give it a listen. If you notice a difference that seems to be worthwhile, leave it powered up. If it does make a difference but you are "frugal", try experimenting with what sounds best left on and what doesn't seem to make much of a difference. You can then power up / shut down as needed. Sean
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