Well, all I know is that violins will develop cracks when the temperature's too high. And when that happens, the violin is stuffed. Ever heard of a piano dehumidifier? Wood will stretch and contract in response to climate. High humidity can damage them permanently (cracks, bridge, soundboard, sticky keys). But these are instruments and I am not quite sure of headphones. If the wood actually plays any part in how the headphone sounds (which I assume they do), then humidity will more likely damage them.
Yes, wood will develop cracks with big variations in temperature, or the temperature is too high. However, if the wood, in this case the violin is protected from temperature variations, then this should not be an issue. Most musical instruments are kept indoors anyway. I suspect you are referring to humidity rather than temperature variation in your comment, just like ryder has suggested.
Yes, I know about piano dehumidifiers. Our Yamaha piano comes with one, though I have yet to check if it's still working. Again, I don't think this humidity thing will affect the wood on the Audeze headphones too much. Perhaps in 10 to 20 years we may see some aging signs, no comment on the cracking part as it depends on the quality and type of wood and how well it's treated. I believe the internal wood of the violin isn't treated and the type of wood is more porous, and perhaps that is where problems crop up with variations in humidity levels.