  We develop a theory for the energy relaxation of hot Dirac fermions in
graphene. We obtain a generic expression for the energy relaxation rate due to
electron-phonon interaction and calculate the power loss due to both optical
and acoustic phonon emission as a function of electron temperature
$T_{\mathrm{e}}$ and density $n$. We find an intrinsic power loss weakly
dependent on carrier density and non-vanishing at the Dirac point $n = 0$,
originating from interband electron-optical phonon scattering by the intrinsic
electrons in the graphene valence band. We obtain the total power loss per
carrier $\sim 10^{-12} - 10^{-7} \mathrm{W}$ within the range of electron
temperatures $\sim 20 - 1000 \mathrm{K}$. We find optical (acoustic) phonon
emission to dominate the energy loss for $T_{\mathrm{e}} > (<) 200-300
\mathrm{K}$ in the density range $n = 10^{11}-10^{13} \mathrm{cm}^{-2}$.
