  The power loss $P$ of hot Dirac fermions through the coupling to the
intrinsic intravalley and intervalley acoustic and optical phonons is
analytically investigated in silicene as a function of electron temperature
$T_e$ and density $n_s$. At very low $T_e$, the power dissipation is found to
follow the Bloch-Gr\"{u}neisen power-law $\propto T_e^4$ and $n_s^{-0.5}$, as
in graphene, and for $T_e \lesssim20-30$ K, the power loss is predominantly due
to the intravalley acoustic phonon scattering. On the other hand,
dispersionless low energy intervalley acoustic phonons begin to dominate the
power transfer at temperatures as low as $\sim$$30$ K, and optical phonons
dominate at $T_e \gtrsim200$ K, unlike the graphene. The total power loss
increases with $T_e$ with a value of $\sim$$10^{10}$ eV/s at $300$ K, which is
the same order of magnitude as in graphene. The power loss due to intravalley
acoustic phonons increases with $n_s$ at higher $T_e$, whereas due to the
intervalley acoustic and optical phonons is found to be independent of $n_s$.
Interestingly, the energy relaxation time in silicene is about $4$ times higher
than that in graphene. For this reason, silicene may be superior over graphene
for its applications in bolometers and calorimeters. Power transfer to the
surface optical phonons $P_{\text{SO}}$ is also studied as a function of $T_e$
and $n_s$ for silicene on Al$_2$O$_3$ substrate and it is found to be greater
than the intrinsic phonon contribution at higher $T_e$. Substrate engineering
is discussed to reduce $P_{\text{SO}}$.
