A model of a stationary glow-type discharge in atmospheric-pressure air operated in high-gas-temperature regimes (1000 K < Tg < 6000 K), with a focus on the role of associative ionization reactions involving N(2D,2P)-excited atoms, is developed. Thermal dissociation of vibrationally excited nitrogen molecules, as well as electronic excitation from all the vibrational levels of the nitrogen molecules, is also accounted for. The calculations show that the near-threshold associative ionization reaction, N(2D) + O(3P) → NO+ + e, is the major ionization mechanism in air at 2500 K < Tg < 4500 K while the ionization of NO molecules by electron impact is the dominant mechanism at lower gas temperatures and the high-threshold associative ionization reaction involving ground-state atoms dominates at higher temperatures. The exoergic associative ionization reaction, N(2P) + O(3P) → NO+ + e, also speeds up the ionization at the highest temperature values. The vibrational excitation of the gas significantly accelerates the production of N2(A3∑u+) molecules, which in turn increases the densities of excited N(2D,2P) atoms. Because the electron energy required for the excitation of the N2(A3∑u+) state from N2(X1∑g+, v) molecules (e.g., 6.2 eV for v = 0) is considerably lower than the ionization energy (9.27 eV) of the NO molecules, the reduced electric field begins to noticeably fall at Tg > 2500 K. The calculated plasma parameters agree with the available experimental data.