The thermal conductivity of individual multiwalled carbon nanotubes was measured by utilizing the four-point-probe third-harmonic method, based on the fact that the third harmonic amplitude and phase as a response to applied alternate current at fundamental frequency, omega, can be expressed in terms of thermal conductivity and diffusivity. To this end, a microfabricated device composed of four metal electrodes was modified to manufacture nanometer-sized wires by using a focused ion beam source. A carbon nanotube could then be suspended over a deep trench milled by the focused ion beam, preventing heat loss to the substrate. Compared with the two-point-probe technique, a significant improvement in accuracy is assured by using four probes, because the contact contribution to the determination of the thermal conductivity is eliminated, making it possible to measure the correct signals of first and third harmonics. The multiwalled carbon nanotube was modeled as a one-dimensional diffusive energy transporter and its thermal conductivity was measured at room temperature under vacuum to be 300 +/- 20 W/mK.