Due to the anti-electromagnetic characteristics, high sensitivity and convenient installation, the Fabry-Perot sensor is commonly used in partial discharge detection of transformers. The variations of eigenfrequency and sensitivity caused by membrane temperature would have an important impact on sensor performance. In the present study, the eigenfrequency and displacement response of an intact membrane (IM) and a beam-supported membrane (BSM) under thermal expansion were numerically studied using a thin film vibration model coupled with temperature variations. The influence of the width and length for BSM’s support beam on the stress softening was also analysed. It is found that the thermal expansion of the membrane reduces the stiffness and both the IM and BSM decrease linearly as temperature increases. The IM and BSM will become unstable as temperature increases to a certain value. The thermal stability of the BSM with support beam structure is lower than that of the IM. When the temperature increases, the IM amplitude increases and the BSM amplitude decreases. The eigenfrequency of the BSM is proportional to the width and inversely proportional to the length of the support beam, while the thermal stability is inversely proportional to the width and length of the support beam.