We report the anisotropic atomic expansion dynamics of multi-walled carbon nanotubes, using 4D electron microscopy. From time-resolved diffraction on the picosecond to millisecond scale, following ultrafast heating at the rate of 10(13) K/s, it is shown that nanotubes expand only in the radial (intertubule) direction, whereas no significant change is observed in the intratubular axial or equatorial dimensions. The non-equilibrium heating occurs on an ultrafast time scale, indicating that the anisotropy is the result of an efficient electron-lattice coupling and is maintained up to equilibration. The recovery time, which measures the heat dissipation rate for equilibration, was found to be on the order of similar to 100 mu s. This recovery is reproduced theoretically by considering the composite specimen-substrate heat exchange.