One of the promising ways to increase fuel and modern gas turbine energy efficiency is using cyclic air intercooling between the stages of high- and low-pressure compressors. For intercooling, it is possible to use cooling in the surface heat exchanger and the contact method when water is injected into the compressor air path. In the presented research on the cooling contact method, it is proposed to use a thermopressor that implements the thermo-gas-dynamic compression process, i.e., increasing the airflow pressure by evaporation of the injected liquid in the flow, which moves at near-sonic speed. The thermopressor is a multifunctional contact heat exchanger when using this air-cooling method. This provides efficient high-dispersion liquid spraying after isotherming in the high-pressure compressor, increasing the pressure and decreasing the air temperature in front of the high-pressure compressor, reducing the work on compression. Drops of water injected into the air stream in the thermopressor can significantly affect its characteristics. An increase in the amount of water increases the aerodynamic resistance of the droplets in the stream. Hence, the pressure in the flow parts of the thermopressor can significantly decrease. Therefore, the study aims to experimentally determine the optimal amount of water for water injection in the thermopressor while ensuring a positive increase in the total pressure in the thermopressor under conditions of incomplete evaporation. The experimental results of the low-consumption thermopressor (air consumption up to 0.52 kg/s) characteristics with incomplete liquid evaporation in the flowing part are presented. The research found that the relative water amount to ensure incomplete evaporation in the thermopressor flow part is from 4 to 10% (0.0175–0.0487 kg/s), without significant pressure loss due to the resistance of the dispersed flow. The relative increase in airflow pressure is from 1.01 to 1.03 (5–10 kPa). Based on experimental data, empirical equations were obtained for calculating the relative pressure increase in the thermopressor with evaporation chamber diameters of up to 50 mm (relative flow path length is from 3 to 10 and Mach number is from 0.3 to 0.8).