How does power/volume effect those times? Or does it not matter?
In my experience, so long as a signal continues to pass through at a whisper the process will progress mostly the same.
When I burn in something I play music for 22 hrs with 2 hours of "rest" to allow everything to cool an settle.
But it wouldn't hurt to play them at different levels at different times of the day. (Whisper at night, low-moderate in the day)
Usually louder levels help more with initial driver break in than crossover burn-in.
Budget parts don't change much over time, just a pretty subtle improvement for the first 50-100 hrs
Higher-end components typically need 200 hrs and will typically follow a process much like Tyson noted.
Anything containing oil or wax (especially caps) will typically need a minimum of 400-500 ours.
Oil & wax damped/impregnated caps can sometimes be rather "unstable" in their sound and can go through several phases of sounding good then bad before they finally get to their gradual improvement phase.
Some brands will tend to be more stable than others.