Superfluid properties of the inner crust of neutron stars. II. Wigner-Seitz cells at finite temperature

We investigate the superfluid properties of the inner crust of neutron stars at finite temperature for different pairing functionals. We generalize the formalism adopted in previous article to include the effect of the temperature to calculate the specific heat of each given Wigner-Seitz cell. The calculations are done for two pairing forces, Gogny D1 and $V_{\text{low-k}}$, with finite range and a density dependent contact interaction. We compare in such a way the effect of the pairing strength and of the range on the thermal properties of the inner crust.