Additional strain increments occur in concrete subject to stress constraints during cold shrinkage, resulting in irregular deformation and reducing the concrete structure's stability. When an annular concrete structure is subjected to radial pressure, two tensile stress concentration zones will appear at the intersection of the inner wall and the diameter along the pressure direction. When exposed to low temperatures, the total strain in the tensile stress concentration zones is caused by the combined effect of applied stress strain and thermal strain. Then, the thermal strain of the structure can be obtained from the difference between the total strain and the applied stress strain. Gradient cooling was performed after applying radial pressure to the annular concrete using a counterforce device. The applied stress strain and total strain of the tensile stress concentration zones are measured by fiber Bragg grating (FBG) strain sensors fixed along the stress direction. According to the measurement results, the thermal strains of the concrete structure under the stress constraint are extracted to analyze the influence of the tensile stress constraint on the thermal strain of the concrete structure. In the temperature range of -40∘C∼20∘C, the thermal strains of the structure under radial pressures of 1500 N, 2000 N, and 3000 N are extracted, respectively. The thermal expansion coefficients are calculated based on the thermal strain of the structure. The free thermal expansion coefficient of concrete structures fluctuates around 11×10-6/∘C. When the temperature is reduced to 10∘C, the difference between the thermal expansion coefficient under the stress constraint and the free thermal expansion coefficient is the largest. When the temperature is reduced to -20∘C, the thermal expansion coefficients under each stress condition are close to the same. The results show that the stress confinement significantly inhibits the cold shrinkage of the concrete structure, and the inhibitory effect is gradually weakened when the temperature decreases.