  The Drude weight for the one-dimensional Hubbard model is investigated at
finite temperatures by using the Bethe ansatz solution. Evaluating finite-size
corrections to the thermodynamic Bethe ansatz equations, we obtain the formula
for the Drude weight as the response of the system to an external gauge
potential. We perform low-temperature expansions of the Drude weight in the
case of half-filling as well as away from half-filling, which clearly
distinguish the Mott-insulating state from the metallic state.
