  We discuss reorganizing finite temperature perturbation theory using
hard-thermal-loop (HTL) perturbation theory in order to improve the convergence
of successive perturbative approximations to the free energy of a gauge theory.
We briefly review the history of the technique and present new results for the
three-loop HTL-improved approximation for the free energy of QED. We show that
the hard-thermal-loop perturbation reorganization improves the convergence of
the successive approximations to the QED free energy at intermediate coupling,
e ~ 2. The reorganization is gauge invariant by construction, and due to
cancellation among various contributions, one can obtain a completely analytic
result for the resummed thermodynamic potential at three loops.
