We analyze the cutoff dependence of the fermion contribution to the finite
temperature free energy density in O(g(2)) lattice perturbation theory for
several improved staggered fermion actions. Cutoff effects are drastically
reduced for the Naik action and an action with improved rotational symmetry
of the quark propagator. We show that improvement of the rotational symmet
ry at O(g(2)) further reduces cutoff effects in thermodynamic observables.
We also show that the introduction of fat links does not have a significant
influence on cutoff distortions at O(g(2)). [S0556-2821(99)06319-5].