  We study the chiral phase transition at finite temperature in the linear
sigma model by employing a self-consistent Hartree approximation. This
approximation is introduced by imposing self-consistency conditions on the
effective meson mass equations which are derived from the finite temperature
one-loop effective potential. It is shown that in the limit of vanishing pion
mass, namely when the chiral symmetry is exact, the phase transition becomes a
weak first order accompanying a gap in the order parameter as a function of
temperature. This is caused by the long range fluctuations of meson fields
whose effective masses become small in the transition region. It is shown,
however, that with an explicit chiral symmetry breaking term in the Lagrangian
which generates the realistic finite pion mass the transition is smoothed out
irrespective of the choice of coupling strength.
