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The effect of thermal treatment at 220 °C for 10 days on the structure and transport properties of a triptycene-based polybenzoxazole (TPBO) was investigated experimentally and theoretically. Gas and water vapor sorption in TPBO is virtually unaffected by thermal treatment, while diffusion and permeability coefficients decrease by just 20%. Remarkably, the CO2/CH4 selectivity exhibit a negligible change. Fluorescence spectroscopy, WAXD and FTIR analysis indicate that, in sharp contrast with typical behavior of glassy polymers, TPBO does not experience accelerated physical aging, and rule out formation of intermolecular charge transfer complexes upon thermal treatment. According with this physical picture, the diffusion coefficient of penetrant molecules sorbed in the Langmuir's mode, DH, does not change after treatment. Small molecule diffusivity and permeability decline is caused by a decrease in polymer chain mobility, which makes more difficult opening gaps to allow penetrant diffusion jumps. According to this picture, the Henry's mode diffusion coefficient, DD, substantially decreases upon thermal treatment. The higher stability exhibited by TPBO relative to other high Tg glassy polymers is ascribed to the presence of configurational free volume, which is not related to the non-equilibrium transient conformation, but to the molecular configuration and, as such, it is not relaxed upon protracted exposure to high temperatures.