This paper studies the difference of non-equilibrium temperatures between constituents, so-called diffusion temperature in the model of mixtures of gases in which each constituent has assigned its own velocity and temperature field. In a previous study (Ruggeri and Simić, Phys. Rev. E 80:026317, 2009), the constitutive equation for the diffusion temperatures, akin to Fick law for the diffusion flux, was derived by means of Maxwellian iteration. In the first order approximation the diffusion temperatures vanish if the constituents have the same ratio of specific heats, i.e. the molecules have the same number of degrees of freedom. This study proceeds to second iteration in the particular case of binary mixture, and provides a second order correction for the diffusion temperature. In this way the classical limit of non-equilibrium temperatures, which covers all the cases, is obtained at the lowest order. A comparison with known results is provided, revealing the corrections and generalizations brought by our results. A special case of constant pressure Fickian diffusion is analyzed and showed that diffusion temperature does not vanish as long as there exist mechanical diffusion between the constituents.