We show that correlators of some local operators in gauge theories are sens
itive to the presence of the instantons even at high temperature where the
latter are bound into instanton-anti-instanton "molecules". We calculate co
rrelation functions of such operators in the deconfined phase of the 2+1 di
mensional Georgi-Glashow model and discuss analogous quantities in the chir
ally symmetric phase of QCD. We clarify the mechanism by which the instanto
n-anti-instanton molecules contribute to the anomaly of axial U(1) at high
temperature.