  We study thermal transport in a one-dimensional (1d) interacting electron
gas, employing the Luttinger liquid model. Both thermal conductance and
thermopower are analyzed for a pure 1d gas and with impurities. The universal
ratio of electrical to thermal conductance in a Fermi-liquid - the
Wiedeman-Franz law - is modified, whereas the thermopower is still linear in
temperature. For a single impurity the Lorenz number is given by $L(T
\rightarrow 0) = 3L_0/(2g+g^2)$ - with $L_0$ the Fermi liquid value - and the
conductance $1/2 < g < 1$. For $g<1/2$ the Lorenz number {\it diverges} as $T
\rightarrow 0$. Possible relevance to thermal transport in conducting polymer
systems is discussed.
