In this paper, a novel arc-shape FBG (Fiber Bragg Grating) load sensor is developed with a pair of FBGs embedded symmetrically in an elastic bending beam. The FBG pair is produced with peak wavelength separation of about 0.4 nm. The FBG with shorter wavelength is located above the neutral layer and another with longer wavelength below the neutral layer. As a result, the two peak wavelengths of the FBG pair move apart with lateral force applied but move together in the same direction when surrounding temperature varies, both in a linear manner. A very low temperature-dependency of only 0.04 pm/°C across the temperature range from 35°C to 82°C has been achieved, which makes it suitable for dynamic lateral force measurement even when the environmental temperature varies. Due to the fact that the sensor module consists of only the grating fiber with two FBGs and some elastic material, which are purely passive components, hence, the temperature effect of this sensor can be self-compensated without a need of any active temperature controller or other temperature-isolation mechanism, thus in principle, this sensor module is passively temperature-independent.