  We study the preheating of gauge fields in a simple axion monodromy model and
compute the induced entropy perturbations and their effect on the curvature
fluctuations. We find that the correction to the spectrum of curvature
perturbations has a blue spectrum with index $n_s = 5/2$. Hence, these induced
modes are harmless for the observed structure of the universe. Since the
spectrum is blue, there is the danger of overproduction of primordial black
holes. However, we show that the observational constraints are easily
satisfied.
