By using the scattering matrix method，the transmission coefficient and thermal conductance of acoustic phonon through a quantum waveguide with semi-circular-arc cavity under both stress-free and hard-wall boundary conditions at low temperatures are studied. The results show that the transmission spectra and thermal conductance exhibit different characteristics under two different boundary conditions. Under the stress-free boundary condition，the universal quantum thermal conductance can be observed regardless of the geometry details in the limit T→0. The quantized plateau is observed only on assuming that the quantum wire is perfect (uniform). For quantum structures with semi-circular-arc cavity，the plateau is destroyed due to the additional scattering induced by the nonuniform waveguide widths to the phonon. When the hard-wall boundary condition is applied，the universal quantum thermal conductance disappears. The thermal conductance increases with the increase of temperature. Moreover，it is found that both the transmission coefficient and thermal conductance can be adjusted by changing the radius of the semi-circular-arc cavity.