We report a periodic thermal cycling method to investigate the dynamic response of the polarization of a laser propagating through polarization-maintaining (PM) optical fiber, driven by periodic weak temperature modulation. Consequently, temperature modulation on the surface of the coating material of the PM fiber was found to cause a continuous periodic change in the polarization state of the output laser without approaching the steady state of the resulting dynamic polarization response. Additionally, the response was found to depend on the temperature-modulation frequency and amplitude. These experimental results are qualitatively in good agreement with that of the simple theoretical model. Our research would be applied not only to the method of measuring properties of a PM optical fiber by utilizing the continuous modulation of the differential refractive index with a wide modulation-frequency range but also to various applications of the dynamic control of the periodic refractive index in materials.