Improved staggered fermion actions for QCD thermodynamics

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 symmetry 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 ${O(g}^2).\mathrm{}$