In this paper, we demonstrate a microwave photonic (MWP) approach for interrogating multiple linearly chirped fiber Bragg grating (LCFBG) temperature sensors. The MWP interrogation system is based on an arrayed waveguide grating Sagnac interferometer, incorporating multiple LCFBG sensors, that is used to generate multiple chirped microwave waveforms whose characteristics are uniquely related to those of the LCFBGs. Compressing the generated microwave signals allows monitoring simultaneously and independently the shifts associated with applying temperature changes to each LCFBG in real time.