  A new perturbative scheme is proposed for the evaluation of the free energy
density of field theories at finite temperature. The screened loop expansion
takes into account exactly the phenomenon of screening in thermal
propagators.The approach is tested in the N-component scalar field theory at
2-loop level and also at 3-loop in the large $N$ limit. The perturbative series
generated by the screened loop expansion shows much better numerical
convergence than previous expansions generated in powers of the quartic
coupling.
