The helium turbine is a critical component of the cryogenic system for nuclear fusion devices. To ensure the turbine's steady functioning and avoid resonance, it is essential to understand and clarify the influence of key factors on its modal characteristics. This paper investigates the influence of thermal effect, fluid-structure interaction and rotational effects on the intrinsic frequency of a helium turbine used in the Comprehensive Research Facility for Fusion Technology (CRAFT) cryogenic system. The effects of coefficient of thermal expansion, thermal conductivity and Young's modulus on the intrinsic frequency of the rotor are explored, considering these thermal factors that vary with temperature. The results indicate that thermal effect has the greatest influence on the intrinsic frequency of the rotor over rotational effectand fluid-structure interaction. Lower-order modes are more sensitive to changes in thermal conductivity, while higher-order modes are more sensitive to changes in Young's modulus at low temperatures. The intrinsic frequency of the rotor is more sensitive to changes in the thermal factors of the shaft rather than the thermal factors of the impellers.