It is  not clear from your question if you want the parameters for a single tube, or for a composite material, or macroscopic material composed of carbon nanotubes. I

f it is a single tube then, yes, you should be able to calculate the phonon spectra etc and then develop models for the thermal conductivity and diffusivity.  

If it is a composite material, or bulk sample composed of CNTs, then you can simulate, but it would likely contain assumptions as to the structure of the material. 

In both cases, experimental verification is needed if the answers are to be relied upon.

 I agree with Dr John Muth.