In this paper, creep-fatigue damage under elevated temperatures is investigated for a tube sheet-to-shell structure, which is one of the main structures under Gen-IV class 1 components. To do this, detailed step-by-step procedures, including the elastic structural analysis and the ASME-NH code application, are described for a defined representative load cycle. From the sensitivity studies for various design parameters, such as hold time duration, shell thickness, and operating temperature, it is found that a reduction of thickness can decrease the thermal bending stresses, but the negative effect is that it may increase the primary stress and enhance the creep damage. The normal operating temperature is the most significant parameter in the creep-fatigue design.