A scanning unbalanced Michelson interferometer is used to act as a demodulator in fiber Bragg grating sensor system. Additional phase-shift, caused by thermal noise, is demonstrated to occur in the output of the interferometer theoretically and experimentally, when a piezoelectric ceramic (PZT) is acted as the driving element of the interferometer. To eliminate the thermal noise, a new method by separating the driving element from the interference device is introduced. Comparing with the conventional with/without temperature controlling interferomtric demodulation scheme, thermal noise is demonstrated to be disappeared experimentally in the new scheme, and there is also no thermal inertia needed to be overcome. The predicted resolution of the system is 5.5 nε, and the experimental sensitivity is 0.9609°/με.