  We present a proof-of-concept experiment aimed at increasing the sensitivity
of temperature sensors implemented with Fiber Bragg gratings by making use of a
weak value amplification scheme. The technique requires only linear optics
elements for its implementation, and appears as a promising method for
extending the range of temperatures changes detectable to increasingly lower
values than state-of the-art sensors can currently provide. The device
implemented here is able to generate a shift of the centroid of the spectrum of
a pulse of $\mathrm{\sim 0.035\,nm/^{\circ}C}$, a nearly fourfold increase in
sensitivity over the same Fiber Bragg Grating system interrogated using
standard methods.
