The articles doesn't really say this. All it really says is that the thermal properties differ dependent on the direction you look at it (in plane (perpendicular to fibre) or transverse (in parallel with the fibres))
But, TL;DR: from the article "Conventional carbon fibre and epoxy layups are poor heat conductors"
As far as I can tell, with laying up carbon fibre on the barrel, the thermal properties are going to depend on the ratio fibres to epoxy, which is dependent on the method of layup. EDIT: Also, because you couldn't (in any cost effective manner) layup carbon fibre on a barrel in plane, all barrels will have carbon fibres layed in the transverse direction - therefore comparing a steel (iron) barrel with a thermal conductivity of 80W/m*K, to a carbon fibre barrel with a thermal conductivity of 8W/m*K - a carbon fibre barrel of equal diameter to a conventional steel barrel is 10 times worse at conducting heat away from the rifling.
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