We investigate how a protein chain achieves the lowest energy state by Monte Carlo simulation using a simple beta-sheet protein model. We show the existence of an optimal temperature range where the energy minimum is found quickly without any exhaustive sorting of the chain conformations even for random sequences. This optimal temperature range is determined by the critical temperature characteristic for the onset of freezing-out of a few lowest-energy chain folds. A simple phenomenological model is presented to account for this behavior of the protein chain.