  We examine the nature of the transitions between the normal and the
superconducting branches of superconductor-graphene-superconductor Josephson
junctions. We attribute the hysteresis between the switching (superconducting
to normal) and retrapping (normal to superconducting) transitions to electron
overheating. In particular, we demonstrate that the retrapping current
corresponds to the critical current at an elevated temperature, where the
heating is caused by the retrapping current itself. The superconducting gap in
the leads suppresses the hot electron outflow, allowing us to further study
electron thermalization by phonons at low temperatures ($T \lesssim 1$K). The
relationship between the applied power and the electron temperature was found
to be $P\propto T^3$, which we argue is consistent with cooling due to
electron-phonon interactions.
