Zuppardi and Verde (Improved Fay-Riddell prcoedure to compute the stagnation point heat flux, Journal of Spacecraft and Rockets 35(3) (1998) 403-405) introduced some operating improvements in the Fay-Riddell computing procedure for the solution of the laminar boundary layer and for the computation of the heat Bur at the stagnation point of spherical bodies in high speed, non-equilibrium dissociating air. Zuppardi and Verde pointed out that the most important improvements were related to the computation both of vibrational temperatures and of Prandtl and Lewis numbers. Vibrational temperatures were computed only as functions of the free stream thermodynamic parameters. Prandtl and Lewis numbers were computed as functions of both the free stream and the local thermodynamic parameters in the boundary layer. The Chapman-Enskog theory with the Lennard-Jones collision integrals were used to compute the transport coefficients. In the present paper the effects of the variability of the vibrational temperatures also in the boundary layer, and of using the more updated collision integrals by Yun and Mason (Collision integrals for the transport properties of dissociating air at high temperature, The Physics of Fluid 5(4) (1962) 380-386) have been evaluated. The results showed that the influence of these factors on the profile of the thermo-fluid-dynamic parameters in the boundary layer was negligible, but it was important on the wall heat flux. The inclusion of the variability of molecular vibration improved the matching both with Navier-Stokes results and experimental data.