  We investigate critical current noise in short ballistic graphene Josephson
junctions in the open-circuit gate-voltage limit within the McWorther model. We
find flicker noise in a wide frequency range and discuss the temperature
dependence of the noise amplitude as a function of the doping level. At the
charge neutrality point we find a singular temperature dependence $T^{-3}$,
strikingly different from the linear dependence expected for short ballistic
graphene Josephson junctions under fixed gate voltage.
