  We analyze a possible superconductivity in the hole-doped system of layered
hydrogenized graphene by taking into account thermal fluctuations of the order
parameter. In particular, we demonstrate that in the one-layer case the values
of the high mean-field (MF) critical temperature $T_{c}^{MF}\sim 80-90K$,
predicted recently by Savini et al \cite{Savini}, do not alter significantly
due to the fluctuations, and the Berezinskii-Kosterlitz-Thouless (BKT) critical
temperature of the vortex superconductivity is almost the same as the MF
temperature at doping 0.01-0.1. We show that in the case of multilayer system,
when the coupling between the layers stabilizes the superconducting phase in
the form of fluxon superconductivity, the critical temperature $T_{c}$ can
increase dramatically to the values $\sim 150K$, higher than the corresponding
values in cuprates under ambient pressure.
