  We study thermal transport in a one-dimensional quantum wire, connected to
reservoirs. Despite of the absence of electron backscattering, interactions in
the wire strongly influence thermal transport. Electrons propagate with unitary
transmission through the wire and electric conductance is not affected. Energy,
however, is carried by bosonic excitations (plasmons) which suffer from
scattering even on scales much larger than the Fermi wavelength. If the
electron density varies randomly, plasmons are localized and {\em charge-energy
separation} occurs. We also discuss the effect of plasmon-plasmon interaction
using Levinson's theory of nonlocal heat transport.
