Higher volume helps best with breaking in Woofers. Since it loosens their suspension ceated by the stiffness of the spider and surround.
With crossover burn in, you don't need volume so much as you just need a good quality signal passing thru them consistently.
I'm currently helping Ron burn in some Tsakiridis Tube amps & preamp, and one of our B-24 power cables and they've been playing non-stop for about 19 days now. (approx 475hrs)
When I'm sleeping, I have them turned down just loud enough to faintly hear them from my bedroom with the door cracked. When i leave for work, I turn them up loud enough to hear the music from any room at more "ambent" levels. Then I'll turn them up a little more once I get back home, and crank them for a bit if I'm in the mood to just listen & sip on coffee, and turn them back down to listening levels at 9pm so I don't disturb the neighbors in my building.
Different components need different levels of break-in/burn-in depending on their electrical properties. Sometimes its a gradual, subtle change, othertimes it's dramatic at first then settles into a gradual change until it completes it's process.
Temperature can definitely also make a difference, esp for tubes.