Abstract: In the present study, a development thermodynamic study of the papers [JNET, 2011, 36 (1), 75-98 and Can. J. of Phy., 2012, 90(2): 137-149] is introduced. The non-stationary BGK (Bhatnager- Gross- Krook) model of the kinetic equations for a rarefied gas mixture affected by nonlinear thermal radiation field is solved instead of the stationary equations. The unsteady solution gives the problem a great generality and more applications. The non-equilibrium thermodynamic properties of the system (gas mixture + the heated plate) is investigated. The entropy, entropy flux, entropy production, thermodynamic forces, kinetic coefficients are obtained for the system. The verification of the Boltzmann H-theorem, Le Chatelier principle, second law of thermodynamic and Onsager's reciprocity relation for the system are made. The ratios between the different contributions of the internal energy changes based upon the total derivatives of the extensive parameters are estimated via the Gibbs formula. The results are applied to the Argon-Neon binary gas mixture, for various values of both of molar fraction parameters and radiation field intensity. 3D-Graphics illustrating the calculated variables are drawn to predict their behavior. The results are discussed.