  We investigate the impacts of neutrino cooling mechanism inside the neutron
star (NS) core on the light curves of type-I X-ray bursts and X-ray
superbursts. From several observations of NS thermal evolution, physical
processes of fast neutrino cooling, such as the direct Urca (DU) process, are
indicated. They significantly decrease the surface temperature of NSs, though
the cooling effect could be suppressed by nucleon superfluidity. In the present
study, focusing on the DU process and nucleon superfluidity, we investigate the
effects of NS cooling on the X-ray bursts using a general-relativistic
stellar-evolution code. We find that the DU process leads find the longer
recurrence time and the higher peak luminosity, which could be obstructed by
the neutrons superfluidity. We also apply our burst models to the comparison
with {\it Clocked burster} GS 1826$-$24, and to the recurrence time of
superburst triggered by carbon ignition. These effects are significant within a
certain range of binary parameters and uncertainty of the NS equation of state.
