  Here, we present the thermal tuning capability of an alignment-free
fiber-integrated Fabry-P\'erot cavity.The two mirrors are made of fiber Bragg
gratings that can be individually temperature stabilized and tuned. We show the
temperature tuning of the resonance wavelength of the cavity without any
degradation of the finesse and the tuning of the individual stop bands of the
fiber Bragg gratings. This not only permits for the cavity's finesse to be
optimized post-fabrication but also makes this cavity applicable as a
narrowband filter with a FWHM spectral width of 0.07 (0.02) pm and a
suppression of more than -15 dB that can be wavelength tuned. Further, in the
field of quantum optics, where strong light-matter interactions are desirable,
quantum emitters can be coupled to such a cavity and the cavity effect can be
reversibly omitted and re-established. This is particularly useful when working
with solid-state quantum emitters where such a reference measurement is often
not possible once an emitter has been permanently deposited inside a cavity.
