Carbon nanotubes can exhibit unique ability to conduct heat. However, the effects of different factors on the thermal conductivity of carbon nanotubes are still poorly understood. The effects of different factors on the thermal conductivity of carbon nanotubes are investigated to understand the mechanisms of transfer of thermal energy through carbon-based materials. Carbon nanotube films and fibers are produced, and the parallel thermal conductance technique is employed to determine the thermal conductivity. The importance of cross-sectional area is determined experimentally. The results indicated that the prepared carbon nanotube films and fibers are very efficient at conducting heat. The structure, purity, and alignment play a fundamentally important role in determining the thermal conductivity of carbon nanotubes. Single-walled carbon nanotube films and fibers generally have high thermal conductivity. The presence of non-carbonaceous impurities degrades the thermal performance due to the low degree of bundle contact. The carbon nanotubes are of the order of several hundred microns, which is significantly greater than the mean free path of phonons. Acoustic phonons exhibit a linear relationship between frequency and phonon wave-vector for long wavelengths. At room temperature, a maximum specific thermal conductivity is obtained but Umklapp scattering occurs. Heat transport in both amorphous and crystalline dielectric solids is by way of elastic vibrations of the lattice. This transport mechanism is theorized to be limited by the elastic scattering of acoustic phonons at lattice defects. The specific thermal conductivity of carbon nanotube fibers is significantly higher than that of carbon nanotube films due to the increased degree of bundle alignment.