This paper focuses on the potential use of stereo-DIC in thermoforming conditions to monitor large deformations of softened thermoplastic sheets posteriori to the sagging phenomenon. The study concerns HIPS sheets which are softened by the radiative heat-transfer mode then stretched by inflation of compressed-air for 1.5 s to form a large and quasi-spherical dome of 250 mm in diameter. While the bubble-inflation operation leads to large deformations of the softened sheet, it shows transitional geometrical instabilities due to the initial surface sagging. When the temperature-induced surface deformations are inaccessible by the stereoscopic system during the heating operation, the geometrical instabilities limit the identification of the reference of displacements which affects the accuracy of results based on image-correlation computations. To compare between the principal strains assessed from bubble-inflation tests conducted at different thermal conditions, a method for filtering these instabilities is developed in this study.