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 micro m(sup 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 approx. 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.