Laser flash and self-heating 3ω techniques were employed to determine the anisotropic thermal conductivity and thermal diffusivity of highly oriented free standing multiwalled carbon nanotube (MWNT) sheet drawn from a sidewall of a MWNT forest that was grown by chemical-vapor deposition. The thermal conductivity and the thermal diffusivity along the alignment are 50±5 W/m·K and 45±5 mm2/s, respectively, and are mostly limited by intrinsic defects of individual nanotubes and phonon-phonon interaction within bundles which form the supporting matrix of the MWNT sheet. The long tube-tube overlapping substantially decreases the electrical and thermal interconnection resistances which are usually dominate in randomly deposited mat-like nanotube assemblies. The extremely large surface area of the MWNT sheet leads to excessive heat radiation that dose not allow to transfer the heat energy by means of phonons to distances > 2 mm.