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Context matters, as does wording. That doesn't look like the wording of a native english speaker, so something may be lost in translation or quotation. Do you have a link to the source so we can judge based on its proper context?
This is why I wanted context - high modulus carbon fibres are good thermal conductors along their length, but not across, especially when embedded in an insulator like epoxy as they often are. Radial fibre arrangements have been proposed, but they're usually too expensive to manufacturer. If someone is manufacturing them now then they may be good thermally as well as structurally. It's about the only way I could see it increasing power handling though, as the more common woven carbon fibre, or carbon fibre loaded paper, won't have that possible thermal advantage. BS from the marketing department seems much more likely, but we'd be in a better position to judge if we could see the original source.
After a short while I went to push on the midrange cone to see if it might be rubbing on a potentially off-center tweeter, but was surprised that the midrange cone was very hot. The midrange driver has a voice coil wound on an aluminum former bonded to an aluminum cone. This gives quite a good heat transfer from coil to cone.
I let it cool down, and repeated the experiment. Same result. In just a matter of 10-15 seconds the cone became very hot.
This is a lot of power being dissipated in the driver. On music I have never noticed that cone getting warm, despite playing at loud levels even in show conditions.
I was on a Rythmik Audio FB page where someone started a thread about a service they can do for your existing speakers. I asked how their cones can increase power handling. She replied that it was her customer that told her that is what it did for his speakers. Then I asked a few more questions ( such as: "how was it measured? who is the customer so I can ask them? are the pictures of your products [cones, finished speaker -it was an Adam Audio monitor] ? ). Then the next time I looked, her complete thread was gone. Probably moderators took it down.