The thermal physics of a massless scalar field with a phi (4) interaction i
s studied within screened perturbation theory (SPT). In this method the per
turbative expansion is reorganized by adding and subtracting a mass term in
the Lagrangian. We consider several different mass prescriptions that gene
ralize the one-loop gap equation to two-loop order. We calculate the pressu
re and entropy to three-loop order and the screening mass to two-loop order
. In contrast with the weak-coupling expansion, the SPT-improved approximat
ions appear to converge even for rather large values of the coupling consta
nt.