The successful operation of a 2 MW 170 GHz coaxial-cavity gyrotron has been demonstrated at IHM-KIT in short(ms) pulses and the ongoing research activities are aiming to upgrade the existing tube to the long-pulse regime. In this work, the performance of the insert cooling system is systematically studied for longpulse coaxial-cavity gyrotron operation. A multi-physics simulation model is developed with the relevant turbulence model and mesh parameters. The results suggest stable operation of the insert under continuous wave (CW) operating condition. In the case of perfectly aligned insert, the maximum temperature of the cooling water is below the boiling temperature and the deformations of the insert geometry are significantly small enough not to influence the performance of the gyrotron. Additionally, the operational limits of the insert cooling system are determined with respect to the maximum allowable heatflux.