The international comparison initiated by the International Temperature Consultative Committee (CCT) aims to collect the latest thermodynamic temperature measurement values of major global temperature measurements, in order to establish the consistency of thermodynamic temperature data among different countries. The international comparison and benchmark-level temperature measurement devices are the core equipment for accomplishing this task, and they rely on cryogenic thermostats to provide an extremely stable temperature environment. This study adopts a numerical simulation method to investigate the behavior of cryogenic thermostats in the international comparison device at thermodynamic temperatures ranging from 5K to 24.5K. The transition from the 5-24.5K international comparison device to the 2-5K benchmark-level temperature measurement device was studied. Firstly, a numerical model of the cryogenic thermostat was established, and this model closely matched the experimental data during the cooling process. Secondly, the cooling process, low-temperature stability, thermal temperature distribution, and resistance characteristics of the cryogenic thermostat were thoroughly studied. The results show that the cooling load caused by radiation heat transfer accounts for a significant proportion of the cryogenic thermostat. Finally, after implementing PID control, the temperature fluctuations in the resonant cavity were successfully controlled within 0.01mK. These research results are of great significance for the design and optimization of international thermodynamic temperature comparison devices, providing valuable guidance for this field.