The carbon nanotube yarns (CNTYs) are directly spun from an aerogel form in a chemical vapor deposition reactor. The as-spun CNTYs are subjected to different post-processes, such as nitric acid treatment, twisting, and doping with iodine. The defect concentrations are detected by Raman spectroscopy, and the effective thermal conductivity is measured by a T-type probe. The results show that, the lattice thermal conductance per unit length decreases smoothly with increasing defects induced by acid treatment and iodine-doping. The twisted yarn introduces moderate defect, but an abnormal decrease in the lattice thermal conductance per unit length is observed as the twist angle increases to ~70°, indicating the phonon-soften phenomenon when CNT is subjected to the torsion stress. The effective thermal conductivity is found to increase linearly as porosity decreases, however, it is still an open question if the linear relationship holds true for highly densified CNTYs.