Gas turbines are important equipment in power grid peak shaving and distributed energy systems, and performance of a gas turbine depends largely on its turbine inlet temperature. Cooling has become one of the most remarkable characteristics of modern gas turbines due to the temperature limitation of materials. Large quantity of cooling air makes the actual cycle of a gas turbine seriously deviating from an ideal Brayton Cycle. Furthermore, use of thermal barrier coating (TBC) adds new characteristic to the heat transfer process, making impact of air cooling on gas turbine performances more complex. However, it still remains a challenge to quantify this impact via a first-principle gas turbine model. In this paper, considering the impact of TBC on the basis of aerothermodynamics calculation, a mathematical model for gas turbine design is proposed. Comparing with performance of a design model without considering TBC impact, results indicate that the proposed modelling approach can improve calculation accuracy of internal energy conversion of a gas turbine.