  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.
