The dynamics of loops at the DNA denaturation transition is studied. A scaling argument is used to evaluate the asymptotic behavior of the autocorrelation function of the state of complementary bases (either open or closed). The long-time asymptotic behavior of the autocorrelation function is expressed in terms of the entropy exponent, c, of a loop. The validity of the scaling argument is tested using a microscopic model of an isolated loop and a toy model of interacting loops. This suggests a method for measuring the entropy exponent using single-molecule experiments such as fluorescence correlation spectroscopy.