  We have considered the dislocation network model for the supersolid state in
He-4 crystals. In difference with uniform 2D and 3D systems, the temperature of
superfluid transition T_c in the network is much smaller than the degeneracy
temperature T_d. It is shown that a crossover into a quasi superfluid state
occurs in the temperature interval between T_c and T_d. Below the crossover
temperature the time of decay of the flow increases exponentially under
decrease of the temperature. The crossover has a continuous character and the
crossover temperature does not depend on the density of dislocations.
