  We study the chiral fermion meson model which is the well known linear sigma
model of Gell-Mann-and-Levy at finite temperature.A modified self-consistent
resummation (MSCR) which resums higher order terms in the perturbative
expansion is proposed. It is shown that with the MSCR the problem of tachyonic
masses is solved, the renormalization of the gap equations is carried out and
the Goldstone's theorem is verified. We also apply the method to investigate
another known case at high temperature and compare with results found in the
literature.
