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The temperature gradient formed by cooling and heat dissipation after shutdown of aero-engine will lead to thermal bending of rotor, which is also the main reason for bending vibration of rotor after engine secondary start-up. In this paper, the rotor system model of a GTF motor considering the gearbox structure is established, and the thermal bending deformation of the fan-gearbox-low pressure rotor caused by temperature gradient is analyzed. The critical speed of the rotor system considering the temperature field is calculated and the vibration characteristics of the engine after the second start are analyzed, which provides a reference for the design of the rotor system of GTF engine. The results show that the rotor mainly appears hot bending deformation in the direction of vertical axis, especially in the joint of disc axis. The large bearing stiffness of the gearbox has obvious inhibition on the hot bending deformation of the rotor, and the effect is obvious when the bearing stiffness is above 1E6. The vibration characteristics of rotor are greatly affected by temperature field. The amplitude of rotor system is larger and the sensitivity of gearbox structure is higher under the influence of temperature field. The amplitude is also the largest when the thermal bending amount is maximum about 10min, and the amplitude decreases by 50% after 40min. The bearing stiffness of the gearbox has a great influence on the vibration characteristics of the rotor system with hot bending deformation, and the vibration suppression effect is best when the bearing stiffness is between 1E6 and 1E8, and the peak point above 1E8 is close to the operating speed of the fan, which is bad for the safe operation of the engine.