We report a single-copy tempering method for simulating large complex systems.In a generalized ensemble,the method uses runtime estimate of the ther-mal average energy computed from a novel integral identity to guide a continuous temperature-space random walk.We first validated the method in a two-dimensional Ising model and a Lennard-Jones liquid system.It was then applied to folding of three small proteins,trpzip2,trp-cage,and villin headpiece in explicit solvent.With-in 0.5 1 microsecond,all three systems were folded into atomic accuracy: the alpha carbon root mean square deviations of the best folded conformations from the native states were 0.2,0.4,and 0.4 ?,for trpzip2,trp-cage,and villin headpiece,respectively.Discussion of folding much larger helical proteins in explicit solvent will also be given.