  We explore the parameter space of the two-flavor thermal quark-meson model
and its Polyakov loop-extended version under the influence of a constant
external magnetic field $B$. We investigate the behavior of the pseudo critical
temperature for chiral symmetry breaking taking into account the likely
dependence of two parameters on the magnetic field: the Yukawa quark-meson
coupling and the parameter $T_0$ of the Polyakov loop potential. Under the
constraints that magnetic catalysis is realized at zero temperature and the
chiral transition at $B=0$ is a crossover, we find that the quark-meson model
leads to thermal magnetic catalysis for the whole allowed parameter space, in
contrast to the present picture stemming from lattice QCD.
