In this paper we examine 9Φ-derivable approximations in QED, General theorems tell us that the gauge dependence of the n-loop Φ-derivable approximation shows up at order g2n where g is the coupling constant. We consider the gauge dependence of the two-loop Φ-derivable approximation to the Debye mass and show that it is of order e4 as expected. We solve the three-loop Φ-derivable approximation in QED by expanding sum-integrals in powers of e2 and m/T, where m is the Debye mass which satisfies a variational gap equation. The results for the pressure and the Debye mass are accurate to order e5. © 2005 The American Physical Society.