An optical fibre Fabry–Perot interferometer (FPI) is proposed and experimentally demonstrated in this work. In the fast Fourier transform spectrum of the FPI transmission spectrum, a higher order model is separated from the transmission spectrum and the spatial frequency spectrum of the higher order model is detected. As the temperature changes, the shifts of the spatial frequency spectrum will be observed. The sensitivity of the temperature is 0.128 μm-1 K-1. The proposed sensor features the advantages of easy fabrication, compact structure and stable chemical property, and exhibits great potential in high-temperature measurement.