In order to capture the behavior of the oxyfuel cycle operating with high combustor-outlet temperature, the impact of blade and vane cooling on cycle performance must be included in the thermodynamic model. As a basis for a future transient model, three thermodynamic models for the cooled gas turbine are described and compared. The first model, known previously from the literature, models expansion as a continuous process with simultaneous heat and work extraction. The second model is a simple stage-by-stage model and the third is a more detailed stage-by-stage model that includes velocity triangles and enables the use of advanced loss correlations. An airbreathing aeroderivative gas turbine is modeled, and the same gas turbine operating in an oxyfuel cycle is studied. The two simple models show very similar performance trends in terms of variation of pressure ratio and turbine inlet temperature in both cases. With the more detailed model, it was found that, without any change of geometry, the turbine rotational speed increases significantly and performance drops for the maintained geometry and pressure ratio. A tentative increase of blade angles or compressor pressure ratio is found to increase turbine performance and decrease rotational speed. This indicates that a turbine will require redesign for operation in the oxyfuel cycle.