  The neutrino-dominated accretion flow (NDAF) with accretion rates \dot{M} =
0.01 - 10 M_{\sun} s^{-1} is a plausible candidate for the central engine of
gamma-ray bursts (GRBs). This hyperaccretion disk is optically thin to
neutrinos in the radial direction, therefore the neutrinos produced at one
radius can travel for a long distance in the disk. Those neutrinos can thus be
absorbed with certain probability by the disk matter at the other radius and
heat the disk there. The effect of this "global neutrino heating" has been
ignored in previous works and is the focus of this paper. We find that around
the "ignition" radius r_{ign}, the global neutrino heating rate could be
comparable to or even larger than the local viscous heating rate thus must be
an important process. Two possible consequences are in order if the "global
neutrino heating" is taken into account: i) the temperature of the disk is
slightly raised and the "ignition" radius r_{ign} slightly shifts to a larger
radius, both lead to the increasing of the total neutrino flux; ii) what is
more interesting is that, the temperature of the ADAF just beyond r_{ign} may
be raised above the virial temperature thus the accretion will be suppressed.
In this case, the activity of the black hole is expected to oscillate between
an active and inactive phases. The timescale of the active phases is estimated
to be \sim 1 second. If the timescale of the inactive phase is comparable to or
less than this value, this intermittent activity may explain the slow
variability component of the GRBs. Self-consistent global calculations of NDAFs
with the "global neutrino heating" included are required in the future to more
precisely evaluate this effect.
