The fundamentals and thermodynamic analysis of high-temperature air combustion (HiTAC) technology is presented. The HiTAC is characterized by high temperature of combustion air having low oxygen concentration. This study provides a theoretical analysis of HiTAC process from the thermodynamic point of view. The results demonstrate the possibilities of reducing thermodynamic irreversibility of combustion by considering an oxygen-deficient combustion process that utilizes both gas and heat recirculations. HiTAC conditions reduce irreversibility. Furthermore, combustion with the use of oxygen (in place of air) is also analyzed. The results showed that a system, which utilizes oxygen as an oxidizer, results in higher first and second law efficiencies as compared to the case with air as the oxidizer. The entropy generation for an adiabatic combustion process is reduced by more than 60% due to the effect of either preheating or oxygen enrichment. This study is aimed at providing technical guidance to further improve efficiency of a combustion process, which shows very small temperature increases due to mild chemical reactions.