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Polarization-maintaining (PM) fiber is the core sensitive component of a fiber optic gyroscope (FOG); its birefringence temperature stability is crucial for maintaining accuracy. Here, we systematically investigated the structural thermal deformation and the resulting birefringence variation in typical PM hollow-core photonic bandgap fibers (HC-PBGFs) for FOG according to varying fiber structure parameters. To verify the application potential of PM HC-PBGFs in FOG, we compared the thermal sensitivity of birefringence (TSB) with that of the commonly used Panda PM fiber, which was tested to 5.07 × 10⁻⁵/100 °C. For rhombic-core fibers, the TSB was determined by the structure of the cladding and could be tuned as low as low as 10⁻⁷/100 °C, two orders of magnitude smaller than that of the panda PM fibers. For hexagonal-core fibers, the birefringence variation depended mainly on the drift of the surface modes (SMs) caused by the deformation of the core. A slight drift in SMs could cause a dramatic birefringence variation in hexagonal-core fiber, and the TSB could be as high as 10⁻⁴/100 °C, much higher than that of panda PM fiber. This study lays the foundation for the development of high birefringence temperature-stable HC-PBGFs and their applications in FOG.