We have proposed a rotor cooling structure using dilute gas for a fully superconducting motor for aircraft application. Numerical analysis was performed to investigate the feasibility of the proposed cooling method and structure, which can make a fully superconducting motor lighter and more compact than a partially superconducting motor. The helium gas pressure in the gap, the rotor rotational speed, and the rotor loss are key parameters of the cooling, and thermal analysis was performed to clarify the dependence of the field winding temperature on these parameters. In the analysis, the motor model has the maximum output of 5.5 MW and the maximum speed of 5000 rpm. The superconducting armature windings are cooled down to 20 K by conduction cooling with liquid hydrogen, and the superconducting field winding is cooled down to about 50 K indirectly using helium gas in the gap. Numerical analysis results indicate that the helium gas pressure should be increased when the rotor loss is larger, but if the pressure is increased too much, the temperature of the field winding becomes higher due to wind loss. When the rotor loss is several hundred watts, the helium gas pressure should be in the range of 104 to 105 Pa.