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.
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.