As a typical engineering structure, the annular concrete structure demonstrates remarkable performance in bearing radial stress and environmental loads. However, when applied to projects in cold areas with large temperature difference between day and night and large seasonal temperature difference, the structure is prone to degradation cracking under the combined action of temperature and external stress, resulting in reduced stability and safety risks. To investigate the complex thermodynamic response of annular concrete structures under the combined constraints of stress and temperature, a detection model was developed to measure structural strain by combining the structural mechanics model with fiber Bragg grating (FBG) detection technology, while a numerical simulation model was created to reflect the mechanical response of the annular concrete structures. Through the performance test of the structure, the bearing capacity range of the structure was determined. Then, the gradient cooling experiments under different stress constraints are carried out to measure the total strain of the structure, extract the thermal strain data and carry out statistical evaluation, and analyze the nonlinear thermal strain response of the structure. The results show that, within the bearing capacity range of 3108 N, the strain of the annular concrete structure gradually increases as the temperature decreases. When the temperature drops from 20 °C to −40 °C, the range of thermal strain initially increases and then decreases. The thermal strain amplitude of the concrete exhibits a significant turning point. Moreover, under different pressure conditions, the thermal strain sensitivity of concrete increases with the gradual increase in pressure confinement, that is, the greater the pressure, the greater the influence on the cooling process of concrete.