  We apply well established finite temperature Quantum Monte Carlo techniques
to one dimensional Bose systems with soft and hardcore constraint, as well as
to spinless fermion systems. We give clear and robust numerical evidence that,
as expected, no superfluid density for Bosons or Meissner fraction for
fermions. is possible at {\em any} non zero temperature in one dimensional
interacting Bose or fermi lattice models, whereas a finite Drude weight is
generally observed in gapless systems, in partial disagreement to previous
expectations.
