  We perform time- and angle-resolved photoemission spectroscopy of a
prototypical topological insulator Bi$_2$Se$_3$ to study the ultrafast dynamics
of surface and bulk electrons after photo-excitation. By analyzing the
evolution of surface states and bulk band spectra, we obtain their electronic
temperature and chemical potential relaxation dynamics separately. These
dynamics reveal strong phonon-assisted surface-bulk coupling at high lattice
temperature and total suppression of inelastic scattering between the surface
and the bulk at low lattice temperature. In this low temperature regime, the
unique cooling of Dirac fermions in TI by acoustic phonons is manifested
through a power law dependence of the surface temperature decay rate on carrier
density.
