  The SU(3)_{r} \times SU(3)_{\ell} linear sigma model is used to study the
chiral symmetry restoring phase transition of QCD at nonzero temperature. The
line of second order phase transitions separating the first order and smooth
crossover regions is located in the plane of the strange and nonstrange quark
masses. It is found that if the U(1)_{A} symmetry is explicitly broken by the
U(1)_{A} anomaly then there is a smooth crossover to the chirally symmetric
phase for physical values of the quark masses. If the U(1)_{A} anomaly is
absent, then there is a phase transition provided that the \sigma meson mass is
at least 600 MeV. In both cases, the region of first order phase transitions in
the quark mass plane is enlarged as the mass of the \sigma meson is increased.
