  Since the invention of the bolometer, its main design principles relied on
efficient light absorption into a low-heat-capacity material and its
exceptional thermal isolation from the environment. While the reduced thermal
coupling to its surroundings allows for an enhanced thermal response, it in
turn strongly reduces the thermal time constant and dramatically lowers the
detector's bandwidth. With its unique combination of a record small electronic
heat capacity and a weak electron-phonon coupling, graphene has emerged as an
extreme bolometric medium that allows for both, high sensitivity and high
bandwidths. Here, we introduce a hot-electron bolometer based on a novel
Johnson noise readout of the electron gas in graphene, which is critically
coupled to incident radiation through a photonic nanocavity. This
proof-of-concept operates in the telecom spectrum, achieves an enhanced
bolometric response at charge neutrality with a noise equivalent power NEP <
5pW/ Sqrt(Hz), a thermal relaxation time of {\tau} < 34ps, an improved light
absorption by a factor ~3, and an operation temperature up to T=300K.
