  The thermal physics of a massless scalar field with a phi^4 interaction is
studied within screened perturbation theory (SPT). In this method the
perturbative expansion is reorganized by adding and subtracting a mass term in
the lagrangian. We consider several different mass prescriptions that
generalize the one-loop gap equation to two-loop order. We calculate the
pressure and entropy to three-loop order and the screening mass to two-loop
order. In contrast to the weak-coupling expansion, the SPT-improved
approximations appear to converge even for rather large values of the coupling
constant.
