In many geotechnical engineering applications, such as nuclear waste disposal and geothermal extraction and storage, it is necessary to consider the long-term mechanical properties. The effect of temperature could have a complicated influence on the creep damage behavior of soft rock. As a consequence, it is meaningful, both in theory and in practice, to establish a constitutive model that can describe the creep damage behavior. Within the framework of continuum mechanics, a thermo-visco-elastoplastic model is proposed on the basis of a sub-loading Cam-clay model and the concept of equivalent stress. Triaxial creep tests under different confining pressures for Tage stone were conducted to validate the proposed model. The experimental results show that an optimum temperature exists for a certain stress state, and this temperature significantly slows down the creep damage rate. In addition, both the retarding and accelerating effects on creep rupture due to limited warming are observed for the same material, and this phenomenon can be predicted well by the proposed model. Finally, a parametric analysis is performed, and the influence of the material parameter on creep regularity is discussed in detail.