  For the deconfining phase of SU(2) Yang-Mills thermodynamics and for high
temperatures we point out that a linear dependence on temperature of a one-loop
selfconsistently resummed thermal correction to the pressure and the energy
density takes place despite a quartic dependence arising from an unsummed
two-loop correction. This linearity is hierarchically smaller than the one
belonging to the tree-level estimate of the thermal ground-state. We discuss
and interprete this result.
