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 i
mplementation, 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.
