Very often carbon fibers are functionalized via sizing. This can be to improve the fiber-matrix bonding and to improve the processing. Sizings are based on epoxy or PU.
Is there any possibility that the sizing will influence the thermal conductivity? So far I am convinced there is no effect as the sizing is very little (< 1% of the fiber) and just used for functionalisation, not to alter someting fundamental on the fiber that will influence the conductivity.