By thermal equilibrium, I mean that the temperature of the casework is no longer changing. In the case of the S300, this is largely to do with the HUGE mass, and the length of time taken to heat through all the cross members and the massive fascia when heat is being lost from the heatsinks.
As this affects the ambient temperature inside the amplifier it will have an impact on the operating temperature of the early stage transistors which are not operating at high currents.
Lots of people have lots of opinions on warm-up and power-up/power down. From measurements I have made temperature has a significant measurable effect on amplifier distortion. For best life of capacitors, keeping a voltage constantly applied to them is much preferable to constant switch on/off.
In terms of "all hifi", because every design is different you can't say things as simply as that. The S300 takes such a long time because of the immense thermal mass. With amplifiers at work I can get them to temperature and optimum performance very quickly if I don't mount the heatsink. If I do, it takes significantly longer to achieve that operating temperature (although the shielding effect of the heatsink has a measureable effect upon dynamic range). Thus, an amplifier with a very small heatsink in a relatively confined space where it will not act efficiently (eg Arcam A65) will get up to temperature very fast compared to an amplifier with very big (3sq ft surface area per channel) and heavy (30kg for the amp) exposed heatsinking like the S300.
A valve obviously requires temperature for its operation. The mass of the valve itself is small and the heat source is very high temperature so it gets up to temperature very quickly. Heatsinking is obviously not applicable.
So, people can believe what they like. Some equipment will act one way, some will act another way. One rule does not apply to all equipment.