We discuss chiral theories of constituent quarks interacting with bosons at high temperatures. In the chirally symmetric phase we demonstrate by applying functional methods the presence of effective anomalous couplings for e.g. πσ → γγ, γ → πππσ, KK → πππσ, etc., as they have recently been discussed by Pisarski. I. INTRODUCTIONIn recent papers [1,2] Pisarski pointed out that although the chiral (abelian as well as nonabelian) anomaly [3,4] in terms of fundamental fields is temperature independent [5,6] the manifestation of the anomaly, however, in terms of effective fields changes with temperature. When considering e.g. π 0 → 2γ the observation in [1,2] is: "In a hot, chirally symmmetric phase, π 0 doesn't go into 2γ, but π 0 σ does"! This statement indeed contradicts results which have been obtained previously [7,8].In [1,2] the effective anomalous couplings for π 0 → 2γ (π 0 σ → 2γ) are found in the framework of the constituent quark model [4,9] by calculating the contribution from the Feynman one-loop triangle (box) diagrams at temperature T = 0 and at nonzero, high T , respectively.In this note we attempt a different approach in order to confirm Pisarski's interesting result. As in [1,2] we start from the linear sigma model with constituent quarks interacting with bosons [10,11]. In order to include the effect of the axial anomaly on the bosons we transform the basis of right-and left-handed quarks following ref. [12], but in the situation of the chirally symmetric phase at high T [13]. At T = 0 and in the spontaneously broken phase this procedure allows a direct calculation of the Wess-Zumino-Witten action [14] for the Goldstone bosons, after applying functional methods for the evaluation of the fermion determinant in connection with path integrals [15].In Sec. II we define the effective lagrangian and describe the way of performing the chirally symmetric limit at high temperature. Sec. III is devoted to the zeta-regularization used to evaluate the fermion determinant in the symmetric case. In Secs. IV and V we discuss the effective anomalous low-energy electromagnetic and hadronic couplings as a result of the chiral anomaly at high T . II. EFFECTIVE CHIRAL LAGRANGIANSWe consider the SU (2) L SU (2) R lagrangian for N C coloured right-and left-handed quarks parametrized in the linear form ("Σ-basis"),with the SU (2) matrix Σ = σ + i τ · π, where we closely follow the notation used in [10]. In the following the explicit form of the boson lagrangian L boson is not needed [10,11]. Although in the strictly symmetric phase the constituent quark mass m has to vanish, we nevertheless introduce explicitly a breaking termWe treat m as an explicit regularization parameter, which is finally removed in the symmetric phase by performing the limit m → 0. However, we do not break the chiral symmetry spontaneously by the standard redefinition of the scalar field σ. * Supported by Deutsche Forschungsgemeinschaft