  Motivated by recent work on inverse magnetic catalysis at finite temperature,
we study the quark-meson model using both dimensional regularization and a
sharp cutoff. We calculate the critical temperature for the chiral transition
as a function of the Yukawa coupling in the mean-field approximation varying
the renormalization scale and the value of the ultraviolet cutoff. We show that
the results depend sensitively on how one treats the fermionic vacuum
fluctuations in the model and in particular on the regulator used. Finally, we
explore a $B$-dependent transition temperature for the Polyakov loop potential
$T_0(B)$ using the functional renormalization group. These results show that
even arbitrary freedom in the function $T_0(B)$ does not allow for a decreasing
chiral transition temperature as a function of $B$. This is in agreement with
previous mean-field calculations.
