  We analyse the effect of neutron superfluidity on the cooling time of inner
crust matter in neutron stars, in the case of a rapid cooling of the core. The
specific heat of the inner crust, which determines the thermal response of the
crust, is calculated in the framework of HFB approach at finite temperature.
The calculations are performed with two paring forces chosen to simulate the
pairing properties of uniform neutron matter corresponding respectively to
Gogny-BCS approximation and to many-body techniques including polarisation
effects. Using a simple model for the heat transport across the inner crust, it
is shown that the two pairing forces give very different values for the cooling
time.
