This paper presents the effects of optical fiber type and copper coating thickness on fiber Bragg grating (FBG) temperature sensitivity. Three types of FBGs including single-mode, step-index, and graded-index multimode fibers were fabricated via the phase mask writing technique. In the temperature range of 30 °C to 80 °C, the step-index multimode FBG exhibits the highest temperature sensitivity of 11.8 pm °C−1 compared to single-mode and graded-index multimode FBG with the sensitivities of 10.5 pm °C−1 and 11.4 pm °C−1, respectively. The temperature sensitivity of the step-index multimode FBG sensor was further improved through the deposition of copper nanolayer which has a greater thermal expansion coefficient than glass. The FBG probe sputtered with a 759.2 nm-thick copper layer achieves the highest temperature sensitivity of 14.2 pm °C−1 compared to those with 306.5 nm and 562.3 nm-thick copper layers which show the sensitivities of 13.2 pm °C−1 and 13.4 pm °C−1, respectively.