We proposed a poly-dimethylsiloxane (PDMS)-coated fiber Bragg grating (FBG) temperature sensor for enhancing temperature sensitivity. By embedding the bare FBG in a temperature-sensitive elastomeric polymer, the temperature sensitivity of the proposed structure could be effectively improved by 4.2 times higher than those of the conventional bare-type FBG sensors due to the high thermal expansion coefficient of the PDMS. We analyzed the temperature-sensitivity enhancement effect with the increased Bragg wavelength shift in our structure and dependence on the temperature sensitivity with respect to the cross-section area of the PDMS.