Kind of guessing why you would want to cold start an amp. If operating costs are an issue, I side with No $. If it's from an eco friendly perspective, consider that the idling provides heat. In the upper midwest we need supplement heat for approx half the year. It's slightly higher $/btu for electricity but so what. If you live in Cal, well then turn everything off to avoid brownouts and surges.
Another consideration, cold starting amps tends to be more stressful on their components. Especially for tubes.
Another consideration, cold starting amps tends to be more stressful on their components. Especially for tubes.