  In this paper we give a detailed analysis of the expected sensitivity and
operating conditions in the power detection mode of a hot-electron bolometer
(HEB) made from a few {\mu}m$^2$ of monolayer graphene (MLG) flake which can be
embedded into either a planar antenna or waveguide circuit via NbN (or NbTiN)
superconducting contacts with critical temperature ~ 14 K. Recent data on the
strength of the electron-phonon coupling are used in the present analysis and
the contribution of the readout noise to the Noise Equivalent Power (NEP) is
explicitly computed. The readout scheme utilizes Johnson Noise Thermometry
(JNT) allowing for Frequency-Domain Multiplexing (FDM) using narrowband filter
coupling of the HEBs. In general, the filter bandwidth and the summing
amplifier noise have a significant effect on the overall system sensitivity.
The analysis shows that the readout contribution can be reduced to that of the
bolometer phonon noise if the detector device is operated at 0.05 K and the JNT
signal is read at about 10 GHz where the Johnson noise emitted in equilibrium
is substantially reduced. Beside the high sensitivity (NEP < 10$^{-20}$
W/Hz$^{1/2}$, this bolometer does not have any hard saturation limit and thus
can be used for far-IR sky imaging with arbitrary contrast. By changing the
operating temperature of the bolometer the sensitivity can be fine tuned to
accommodate the background photon flux in a particular application. By using a
broadband low-noise kinetic inductance parametric amplifier, ~100s of graphene
HEBs can be read simultaneously without saturation of the system output.
