  Combining the Bethe Ansatz with a functional deviation expansion and using an
asymptotic expansion of the Bethe Ansatz equations, we compute the curvature of
levels D_n at any filling for the one-dimensional lattice spinless fermion
model. We use these results to study the finite temperature charge stiffness
D(T). We find that the curvature of the levels obeys, in general, the relation
D_n=D_0+\delta D_n, where D_0 is the zero-temperature charge stiffness and
\delta D_n arises from excitations. Away from half filling and for the
low-energy (gapless) eigenstates, we find that the energy levels are, in
general, flux dependent and, therefore, the system behaves as an ideal
conductor, with D(T) finite. We show that if gapped excitations are included
the low-energy excitations feel an effective flux \Phi^{eff} which is different
from what is usually expected. At half filling, we prove, in the strong
interacting limit and to order 1/V (V is the nearest-neighbor Coulomb
interaction), that the energy levels are flux independent. This leads to a zero
value for the curvature of levels D_n and, as consequence, to D(T)=0, proving
an earlier conjecture of Zotos and Prelov\v{s}ek.
