We demonstrate that the resonance wavelength of fiber Bragg gratings photowritten in the core of microstructured optical fibers can be efficiently stabilized versus temperature by inserting suitable refractive index materials with a negative thermal sensitivity into the holes. By these means, the effective index of the guided mode undergoes thermal variations which counterbalance the effect of the grating period thermal drift. The residual excursion of the resonance wavelength can be limited to less than +/- 10 pm over a 70 degrees C range of temperature into Microstructured Optical Fibers (MOFs) having realistic geometrical parameters, and using existing refractive index materials. Low cost passively stabilized reflectors with insertion loss lower than 0.3 dB can be realized by splicing single mode fibers at both ends of a short length of a filled MOF including the fiber Bragg grating.