  Using conformal perturbation theory, we show that for some classes of the
one-dimensional quantum liquids that possess the Luttinger liquid fixed point
in the low energy limit, the Drude weight at finite temperatures is
non-vanishing, even when the system is {\it non-integrable} and the total
current is not conserved. We also obtain the asymptotically exact
low-temperature formula of the Drude weight for Heisenberg XXZ spin chains,
which agrees quite well with recent numerical data.
