In this letter, we study the phonon ballistic transmission and the thermal conductivity in a dielectric quantum waveguide with one or two defect regions. The results show that these observable quantities strikingly depend on geometric parameters, and are of quantum character. The total transmission coefficient versus the reduced waveguide-length exhibits periodical behavior. Our results also show that one can control the thermal conductivity of the structure and make different acoustic filters by adjusting the geometric parameters. (C) 2007 Elsevier Ltd. All rights reserved.