  We study the restoration of chiral symmetry in linear sigma models with two
quark flavors. The models taken into consideration have a U(2)_L x U(2)_R and
an O(4) internal symmetry. The physical mesons of these models are sigma, pion,
eta and a_0 where the latter two are not present in the O(4) model. Including
two-loop contributions through sunset graphs we calculate the temperature
behavior of the order parameter and the masses for explicit chiral symmetry
breaking and in the chiral limit. Decay threshold effects introduced by the
sunset graphs alter the temperature dependence of the condensate and
consequently that of the masses as well. This correctly reproduces a
second-order phase transition for the O(4) model and for the U(2)_L x U(2)_R
model with an axial U(1) anomaly as expected from universality class arguments.
Chiral symmetry tends to be restored at higher temperatures in the two-loop
approximation than in the Hartree-Fock approximation. To model a restoration of
the axial U(1) symmetry we imply a temperature-dependent anomaly parameter that
sharply drops at about 175 MeV. This triggers the restoration of chiral
symmetry before the full symmetry is restored and lowers the transition
temperatures significantly below 200 MeV.
