A gas turbine air bottoming cycle consists of a gas turbine unit and the air turbine part. The air part includes a compressor, air expander and air heat exchanger. The air heat exchanger couples the gas turbine to the air cycle. Due to the low specific heat of air and of the gas turbine exhaust gases, the air heat exchanger features a considerable size. The bigger the air heat exchanger, the higher its effectiveness, which results in the improvement of the efficiency of the gas turbine air bottoming cycle. On the other hand, a device with large dimensions weighs more, which may limit its use in specific locations, such as oil platforms. The thermodynamic calculations of the air heat exchanger and a preliminary selection of the device are presented. The installation used in the calculation process is a plate heat exchanger, which is characterized by a smaller size and lower values of the pressure drop compared to the shell and tube heat exchanger. Structurally, this type of the heat exchanger is quite similar to the gas turbine regenerator. The method on which the calculation procedure may be based for real installations is also presented, which have to satisfy the economic criteria of financial profitability and cost-effectiveness apart from the thermodynamic criteria.