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 μm<sup>2</sup> 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<sup>-20</sup> W/Hz<sup>1/2</sup>), 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.