We analyze and predict the performance of a fiber-optic temperature sensor from the measured fluorescence spectrum to optimize its design. We apply this analysis to an erbium-doped silica fiber by employing the power-ratio technique. We develop expressions for the signal-to-noise ratio in a band to optimize sensor performance in each spectral channel. We improve the signal-to-noise ratio by a factor of 5 for each channel, compared with earlier results. We evaluate the analytical expression for the sensor sensitivity and predict it to be approximately 0.02 degrees C(-1) for the temperature interval from room temperature to above 200 degrees C, increasing from 0.01 degrees C(-1) at the edges of the interval to 0.03 degrees C(-1) at the center, at 100-130 degrees C. The sensitivity again increases at temperatures higher than 300 degrees C, delineating its useful temperature intervals.