Most amplifiers, or at least output stages, are burned in at the factory, on "burn in racks." I worked for manufacturers for decades, and I was involved in product development in addition to sales and marketing. Amps are burned in so if they fail, they will fail before being shipped and sold. Components seem to fail early, and if they don't, they usually will last for many years. I have never witnessed a break-in period where an amplifier was transformed over 400 hours from a strident banshee to a smooth, natural sweetheart. It doesn't happen.
That said, playing a cold amplifier hard is a bad idea because the temperature difference between the inside and outside of some components (output transistors, for example) may be too great and cause microscopic cracks to develop. Play an amp at a moderate level for ten minutes before beating on it. Some amplifiers, as long as they're plugged in, draw a small amount of current in stand-by mode, keeping circuits ready but outputs muted. Recent RoHS requirements state that amplifiers can't draw much current at idle anymore. We used to let amps idle at 100 watts power consumption so they sounded good from the first note, and in retrospect, that was ridiculous. Amplifiers were often over-biased and they idled red hot. Heat over time kills amplifiers. Also, the violence of turning an amp on doesn't help it, either. I usually don't ever turn mine off; vintage McIntosh or super-modern Lyngdorf semi-digital. If I know I won't be playing any of my systems for a few days, then I shut them down.
If an amp has been outside in cold weather, let it sit inside for a day before even plugging it in. If you turn a system on, don't play the bejeezus out of it until semiconductors have been brought up to optimum temperature.