Recently, a two-temperature transport properties theory has been proposed that retains the coupling between electrons and heavy species in thermal plasmas where the kinetic temperature of electrons T(e) can be different from that of heavy species T(h). This paper is devoted to the application of this approach to an argon-hydrogen mixture at atmospheric pressure, taking into account inelastic processes and considering chemical equilibrium. In this second part are studied: . the development of a new method to calculate the reaction thermal conductivity (inelastic collisions) in a non-equilibrium (two-temperature) plasma taking into account the coupling between electrons and heavy species; . the influence of the composition calculation methods comparing the modified equilibrium constant method used in part 1 to the stationary kinetic calculation one; . the influence on the transport properties (sigma, mu, kappa) of the composition calculation method and non-equilibrium parameter theta = T(e)/T(h). The different plasma compositions obtained either through an equilibrium constant or a stationary kinetic method are first compared and, for example, for theta = 1.6, a discontinuity at T(e) = 11,000 K and an ionization delay are observed in stationary kinetic calculation, relative to the equilibrium constant method. Electrical conductivity, viscosity as well as thermal conductivity, including the translational, internal and reactional contributions, are calculated up to 25,000 K. It is shown that the plasma composition has a strong influence on transport coefficients, inducing shifts or discontinuities in the curves of transport coefficients, depending on the chosen method of calculation.