The three-body recombination of oxygen atoms O + O + M → O ₂(el) + M is the dominant process of oxygen excitation in the Earth's nightglow at altitudes of 85–110 km. The rate coefficient of this reaction, as well as the quantum yields of electronically excited products (O ₂(el) in the electronic states: ⁵π _g, A ³Σ _u ⁺, A′ ³Δ _u, c ¹Σ _u ⁺, b ¹Σ _g ⁺, a ¹Δ _g, X ³Σ _g ^-) depend on the gas kinetic temperature. In addition to the direct one-stage excitation channel of these levels of the O ₂ molecule, the Barth's mechanism considers the two-stage energy transfer channel. In this channel, higher excited levels of the O ₂ act as precursors for the excitation of the O( ¹S) atom and the underlying electronic levels of the O ₂. In this study, we use sensitivity analysis to consider the temperature dependence of the processes of excitation and quenching for each of the excited components. The analytical expressions are obtained for the sensitivity coefficients of the Volume Emission Rates depending on temperature for the green line of atomic oxygen O( ¹S → ¹D), the Herzberg I band O ₂(A ³Σ _u ⁺→X ³Σ _g ^-) and O ₂ Atmospheric band O ₂(b ¹Σ _g ⁺,v ^'=0→X ³Σ _g ^-, v ^''=0). With the help of the sensitivity analysis performed in this work, we (a) confirm that the state O ₂( ⁵π _g), produced by the three-body recombination of atomic oxygen, is a precursor for the formation of O ₂(b ¹Σ _g ⁺), (b) estimate the quantum yield of the O ₂(b ¹Σ _g ⁺) state formed as a result of collisional reaction O ₂( ⁵π _g) with O ₂, and (c) propose a method for determining a type of precursor for production of O( ¹S) in the Barth's mechanism.