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The work is d to improving methods for calculating the cooling system of a microturbine with a rotor on air bearings. When designing gas turbines, it is important to integrate gas-dynamic calculations with thermal finite-element calculations. In practice, the conjugation of temperature fields in solids and liquids, as well as the transfer of thermal loads between the media are carried out using several approaches: direct, non-conjugate and sequential coupled. Numerical simulation of the coupled heat transfer in a cavity formed by the gap between the rotor and stator is carried out. To calculate the flow characteristics of a viscous compressible fluid and heat transfer. The degree of influence on the results of the type of turbulence model used, the influence of taking into account the conjugate heat transfer, is studied. The effect of the mass flow rate of the cooler on the flow structure and the cooling efficiency of the walls of the rotor and stator is investigated. A comparison is made with experimental data. Numerical experiments have shown that in typical cases the flow in the cavity is turbulent. The cooling efficiency has a limit on the flow rate of the cooler. The temperature distribution along the length of the rotor has a noticeable minimum in the region of the middle of the length of the rotor. The significance of the obtained results lies in the fact that the choice of the turbulence model weakly affects the calculation results and taking into account the conjugate nature of heat transfer is necessary.