A signal processing method for white light interferometry (WLI), which performs a series of analog signal processing steps to locate the central interference fringe position at high speed: is developed and applied to a WLI temperature sensor system. We found that the new method has random walk of $0.019^{circ}C/sqrt{Hz}$ with good linearity. However, the temperature change in the path-matching interferometer results in drift of the measured sensor output. The temperature dependence of drift in the WLI temperature sensor system, was calculated to be $1.42{mu}m/^{circ}C$. It is also found that the relationship between the peak spacing in the interferogram and the spacing measured by the method can be nonlinear when the fringe spacing is comparable to the coherence length of the source.