  We analyze the cut-off dependence of mesonic spectral functions calculated at
finite temperature on Euclidean lattices with finite temporal extent. In the
infinite temperature limit we present analytic results for lattice spectral
functions calculated with standard Wilson fermions as well as a truncated
perfect action. We explicitly determine the influence of `Wilson doublers' on
the high momentum structure of the mesonic spectral functions and show that
this cut-off effect is strongly suppressed when using an improved fermion
action.
