The influences of the pump wavelength and temperature on the dual-peaked Brillouin property of a piece of a small-core microstructure fiber are investigated using the heterodyne method. The experimental results indicate that the dispersion characteristics of the acoustical modes participating in the Brillouin scattering are formed by the coupling of two acoustical modes with different acoustical field distributions. The influence of the pump wavelength can contribute to the variation of the acoustical mode wave vectors. On the other hand, the influence of the environment temperature can contribute to the shift of acoustical mode dispersion map by the variation of the material mechanical parameters and thermal expansion. The model and experiment results demonstrate that the height ratio of the two Brillouin peaks can be controlled by adjusting the pump wavelength or environment temperature.