Improved Staggered Fermion Actions for QCD Thermodynamics

We analyze the cut-off dependence of the fermion contribution to the finite temperature free energy density in $\mathcal{O}(g^2)$ lattice perturbation theory for several improved staggered fermion actions. Cut-off effects are drastically reduced for the Naik action and an action with improved rotational symmetry of the quark propagator. We show that improvement of rotational symmetry at ${\cal O}(g^2)$ further reduces cut-off effects in thermodynamic observables. We also show that the introduction of fat-links does not have a significant influence on cut-off distortions at $\mathcal{O}(g^2)$.