By using the scattering matrix method, the transmission coefficient and thermal conductance of acoustic phonon through a quantum waveguide with abrupt quantum junctions modulated with double T-shaped quantum structure at low temperatures are studied. The results show that at very low temperatures, the double T-shaped quantum structure can enhance low-temperature thermal conductance; contrarily, at higher temperatures, the double T-shaped quantum structure can reduce low-temperature thermal conductance. However, in the whole low-temperature region, the low-temperature thermal conductance can be enhanced by adding the narrowest width c in the scattering region. Moreover, it is found that both the transmission coefficient and thermal conductance can be adjusted by changing the structural parameters of the the scattering region.