Modern gas turbines firing temperatures (1500-2000K) are well beyond the maximum allowable blade material temperatures. Continuous safe operation is made possible by cooling the HP turbine first stages -nozzle vanes and rotor blades- with a portion of the compressor discharge air, a practice that induces a penalty on the cycle thermal efficiency. Therefore, a current issue is to investigate the real advantage, technical and economical, of raising maximum temperatures much further beyond current values. In this paper, process simulations of a gas turbine are performed to assess HP turbine first-stage cooling effects on cycle performance. A new simplified and properly streamlined model is proposed for the non-adiabatic expansion of the hot gas mixed with the cooling air within the blade passage, which allows for a comparison of several cycle configurations at different TIT (turbine inlet temperature) and max (total turbine expansion ratio) with a realistically acceptable degree of approximation.. The calculations suggest that, at a given max, the TIT can be increased in order to reach higher cycle efficiency up to a limit imposed by the required amount and temperature of the cooling air. Beyond this limit, no significant gains in thermal efficiency are obtained by adopting higher max and/or increasing the TIT, so that it is convenient in terms of cycle performance to design at lower rather than higher max. The small penalty on cycle efficiency is compensated by lower plant cost. The results of our model agree with those of some previous much more complex and computationally expensive studies, so that the novelty of this paper lies in the original method adopted on which the proposed model is based, and in the fast, accurate and low resource intensity of the corresponding numerical procedure: all advantages that can be crucial for industry needs. The presented analysis is purely thermodynamic, with no investigation on the effects of the different configurations on plant costs, so that future work addressing a thermo-economic analysis of the air-cooled gas turbine power plant is the next logical step.