1. Rigorous calculation: adiabatic flame temperature energy equation
   At reference temperature $T_0$, with LHV $Q_{LHV}$ (kJ/kg fuel), energy conservation:

• $Q_{LHV} + \sum n_r h_r(T_{in}) = \sum n_p h_p(T_{ad})$

If feeds are near $T_0$, it can be written in temperature-rise form:

• $Q_{LHV} = \sum n_p \int_{T_0}^{T_{ad}} c_{p,p}(T)\,dT$
  At high temperature, dissociation and temperature dependence of $c_p(T)$ must be considered.

2. Engineering approximation: estimate using average constant-pressure specific heat

• $T_{ad} \approx T_0 + \dfrac{Q_{LHV}}{\sum n_p \bar c_{p,p}}$
  Where $\bar c_p$ is the average value from $T_0$ to $T_{ad}$. This is used for quick estimation and trend judgment.

3. Direct rewrite for influencing terms (common refinements)

• With air preheat: $Q_{eff} = Q_{LHV} + \sum n_{air}\int_{T_0}^{T_{air}} c_{p,air} dT$
• With $\alpha>1$: more $N_2$ and excess $O_2$ in products increases $\sum n_p \bar c_p$, so $T_{ad}$ decreases.