In energy geostructures, the soil-structure interface is subjected to thermo-mechanical loads. In this study, a non-isothermal soil-structure interface model based on critical state theory is developed from a granular soil-structure interface constitutive model under isothermal conditions. The model is capable of capturing the effect of temperature on sand/clay-structure interfaces under constant normal load and constant normal stiffness conditions. First, the developed model was verified for sand-structure interface in isothermal conditions. Then, it was calibrated for clay-structure interface under non-isothermal conditions. On one hand, a well-defined peak shear stress for the clay-structure interface and, on the other hand, the effect of temperature on the void ratio of the clay-structure interface were captured and reproduced by the model. The importance of interface thickness determination and some differences between the interface thicknesses of clay-structure and sand-structure interfaces are discussed in detail. The additional parameters have physical meanings and can be determined from laboratory tests. The modeling predictions are in good agreement with experimental results, and the main trends are properly reproduced.