Improved ground-state estimate by thermal resummation

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.