  We study the thermodynamics of QCD in the limit of large flavor number (N_f)
and test the proposal to resum the physics of hard thermal loops (HTL) through
a nonperturbative expression for the entropy obtained from a Phi-derivable
two-loop approximation. The fermionic contribution to the entropy involves a
full next-to-leading order evaluation of the asymptotic thermal quark mass,
which is non-local, and for which only a weighted average value was known
previously. For a natural choice of renormalization scale we find remarkably
good agreement of the next-to-leading-order HTL results for the fermion self
energy and in turn for the entropy with the respective exact large-N_f results
even at very large coupling.
