We propose a white-light interferometric demodulation algorithm for high-finesse fiber-optic F-P sensors, in order to improve the demodulation accuracy and the dynamic range encountered in traditional demodulation techniques. The interferometric spectral signal of the high-finesse F-P cavity was converted to the frequency domain and then a more accurate cavity length was estimated based on full phase on higher-order components. A detailed theoretical analysis was operated. A high-finesse F-P temperature sensor based on a silicon diaphragm was fabricated and tested to verify the proposed method. The demodulation accuracy increases with the increase of order, and the anti-noise performance is improved. For the third-order component, the optical path difference sensitivity obtained by this algorithm is 0.231 ± 0.0188 μm / ° C, and the average error rate of cavity length demodulation value is 0.0152%. The proposed algorithm is applicable to demodulate the high-finesse F-P cavities in the light source bandwidth of 1525 to 1575 nm, providing high accuracy and improved anti-noise performance.