I think what you are hearing isn't speakers warming up; rather it is your amplifier warming up.
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Good question. I've never seen or heard of a speaker manufacturer talk about "warm up time." It makes sense to me, but I tend to agree with Beavis that the amps, and possibly the pre (provided your using a pre)(and even with standby mode), are still warming up.
Especially if your running large monoblocks.
Of course, I only listen to music whilst sipping my favorite beverage.
And the more I sip, the better it sounds (usually). ;-)
I doubt that there is much warmup for speakers. Conceivably, the suspension parts (surround, the spider, etc.) could be warmed by friction, but I have never heard of that making an appreciable difference. The voice coil itself is NOT a moving part in that it should not be rubbing against anything so there is no issue of a change in friction coefficient.
If anything, the resistive heating of the voice coil from usage should detract from sound quality by causing compression. As the coil warms up resistance increases and the output of the driver will fall. I would expect hard usage to temporarily adversely affect the sound quality, not improve the sound.
Audioholics did an interesting piece on measuring cone movements and frequency responses with and without break in.
Their conclusion: no difference. But, it still comes down to the "objectivists vs. the subjectivists" argument. Your ears and brain are the only important criteria.
Sure, speaker probably do have a warm up time. Many contain capacitors, resistors and inductors that change as signal passes through them.
My Sound-Labs were very slow to warm up in spite the amount of time the electronics had been on. Sound-Labs back plates contain two large transformers, (one EI and one Toroidal). Also, 8 or more resistors (depending on which version you have), a brilliance control, switches for mid and bass EQ and several caps. All these are in the signal path.
No doubt there are other examples of speakers with similar parts, even if much fewer that this example.
As for the voice coil improving or suspension freeing up too? Could be, I would not argue with anyone who says it does.
My system overall needs about eight hours to fully open up.
It's easy to know, it always sounds thin, closed and clouded when first started and the next morning is wide open when I leave in on overnight.
The speakers have two internal digital amps each. And when I turn them off and restart them, there is a noticable choking of the sound. It generally takes a few hours to return to the prior sound.
So, I leave the system on fulltime except during electrical storms.