  Electronic cooling in hybrid normal metal-insulator-superconductor junctions
is a promising technology for the manipulation of thermal loads in solid state
nanosystems. One of the main bottlenecks for efficient electronic cooling is
the electron-phonon coupling, as it represents a thermal leakage channel to the
phonon bath. Graphene is a two-dimensional material that exhibits a weaker
electron-phonon coupling compared to standard metals. For this reason, we study
the electron cooling in graphene-based systems consisting of a graphene sheet
contacted by two insulator/superconductor junctions. We show that, by properly
biasing the graphene, its electronic temperature can reach base values lower
than those achieved in similar systems based on metallic ultra-thin films.
Moreover, the lower electron-phonon coupling is mirrored in a lower heat power
pumped into the superconducting leads, thus avoiding their overheating and
preserving the cooling mechanisms. Finally, we analyze the possible application
of cooled graphene as a bolometric radiation sensor. We study its main figures
of merit, i.e. responsivity, noise equivalent power and response time. In
particular, we show that the built-in electron refrigeration allows reaching a
responsivity of the order of 50 nA/pW and a noise equivalent power of order of
$\rm 10^{-18}\, W\, Hz^{-1/2}$ while the response speed is about 10 ns,
corresponding to a thermal bandwidth in the order of 20MHz.
