The intrinsic thermal conductivity of an individual carbon nanotube and its contact thermal resistance with the heat source/sink can be extracted simultaneously through multiple measurements with different lengths of the tube between the heat source and the heat sink. Experimental results on a 66-nm-diameter multiwalled carbon nanotube show that above 100 K, contact thermal resistance can contribute up to 50% of the total measured thermal resistance; therefore, the intrinsic thermal conductivity of the nanotube can be significantly higher than the effective thermal conductivity derived from a single measurement without eliminating the contact thermal resistance. At 300 K, the contact thermal resistance between the tube and the substrate for a unit area is 2.2 × 10−8 m2 K W−1, which is on the lower end among several published data. Results also indicate that for nanotubes of relatively high thermal conductance, electron-beam-induced gold deposition at the tube–substrate contacts may not reduce the contact thermal resistance to a negligible level. These results provide insights into the long-lasting issue of the contact thermal resistance in nanotube/nanowire thermal conductity measurements and have important implications for further understanding thermal transport through carbon nanotubes and using carbon nanotube arrays as thermal interface materials.