A nonlinear temperature sensor was proposed drawing on dispersive wave (DW) and soliton in an in-house made silica microstructured optical fiber (MOF). Glycerin with high thermo-optical coefficient was filled into the MOF air holes as the thermal medium. Using a 1050 nm femtosecond laser as the pump source, DW and soliton were experimentally and theoretically explored for temperature sensing by detecting their central wavelength shift of 3-dB bandwidth. The results showed that the higher the average pump power, the higher the temperature sensitivity of DW and soliton. When the DW blue-shifted relative to the soliton, the temperature sensitivity of DW was higher than that of soliton, and the experimental maximum values were 0.928 nm/℃ (DW) and -0.923 nm/℃ (soliton). Our work explored the nonlinear phenomenon for optical fiber-based sensing technology and verified that both DW and soliton can be used to realize temperature sensors of high sensitivity and good mechanical strength. The sensing characteristic difference of DW and soliton revealed in this work might provide a new way for solving the cross-sensitivity of dual-parameter sensing in biological engineering, disease detection and environmental monitoring without introducing extra structural complexity.