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.
