  We analyse the finite temperature charge stiffness D(T>0), by a
generalization of Kohn's method, for the problem of a particle interacting with
a fermionic bath in one dimension. We present analytical evidence, using the
Bethe ansatz method, that D(T>0) is finite in the integrable case where the
mass of the particle equals the mass of the fermions and numerical evidence
that it vanishes in the nonintegrable one of unequal masses. We conjecture that
a finite D(T>0) is a generic property of integrable systems.
