This paper is an analysis of temperature and birefringence fluctuation effects on the operation of a Sagnac fiber optic gyroscope. The temperature fluctuations and vibrations cause the optical path length of the light waves within the fiber to fluctuate, and this in turn causes the phase of the optical waves to vary in a random fashion. The random phase variations are a noise source in the gyro and the magnitude of the effect depends upon the demodulation technique used to determine the Sagnac phase shift.