The thermal ageing of a silane-crosslinked polyethylene stabilised with 1 wt% of distearyl thiodipropionate (Irganox PS802) was studied in air at three different temperatures: 87 °C, 110 °C, and 130 °C. FTIR spectroscopy and DSC under O2 were used in a complementary way to monitor the antioxidant (AO) depletion during thermal ageing, but also to detect the polymer oxidation. In particular, at the three ageing temperatures under study, it was observed that the physical loss of AO is the main ageing mechanism and is controlled by AO evaporation. However, the contribution of the AO chemical consumption in the overall kinetics of AO depletion was also estimated. In addition, the temperature dependences of the evaporation constant and the rate constant of the chemical consumption of AO were approximated with the usual Arrhenius law in the temperature range under investigation. Although the corresponding activation energies must be considered with caution, due to the limited amount of data acquired in this study, they were found to be in good agreement with the few results available in the literature.