We perform a generalized-ensemble simulation of a small peptide taking the interactions among all atoms into account. From this simulation we obtain thermodynamic quantities over a wide range of temperatures. In particular, we show that the folding of a small peptide is a multistage process associated with two characteristic temperatures, the collapse temperature to and the folding temperature T(f). Our results give supporting evidence for the energy landscape picture and funnel concept. These ideas were previously developed in the context of studies of simplified protein models, and here are checked in an all-atom Monte Carlo simulation.