  We present a detailed study on the properties of the free energy density at
the high temperature by applying the principle of maximum conformality (PMC)
scale-setting method within the effective field theory. The PMC utilizes the
renormalization group equation recursively to identify the occurrence and
pattern of the non-conformal $\{\beta_i\}$-terms, and determines the optimal
renormalization scale at each order. Our analysis shows that a more accurate
free energy density up to $g_s^5$-order level without renormalization scale
dependence can be achieved by applying the PMC. We also observe that by using a
smaller factorization scale around the effective parameter $m_E$, the PMC
prediction shall be consistent with the Lattice QCD prediction derived at the
low temperature.
