The heat transport through one-dimensional quantum wire is considered in the frameworks of the inhomogeneous Tomonaga–Luttinger liquid model. It is shown that even for perfect (impurity free) wire thermal transport is suppressed due to multiple scattering of plasmons on the boundaries that connect quantum wire to the leads of noninteracting electrons. In the presence of impurity inside the Luttinger liquid constriction resonant enhancement of thermal conductivity at certain conditions is predicted. ©1998 American Institute of Physics.