We show that a single-copy tempering method is useful in protein-folding simulations of large scale and high accuracy (explicit solvent, atomic representation, and physics-based potential). The method uses a runtime estimate of the average potential energy from an integral identity to guide a random walk in the continuous temperature space. It was used for folding three mini-proteins, trpzip2 (PDB ID: 1LE1), trp-cage (1L2Y), and villin headpiece (1VII) within atomic accuracy. Further, using a modification of the method with a dihedral bias potential added on the roof temperature, we were able to fold four larger helical proteins: α3D (2A3D), α3W (1LQ7), Fap1-NRα (2KUB) and S-836 (2JUA). We also discuss how to optimally use simulation data through an integral identity. With the help of a general mean force formula, the identity makes better use of data collected in a molecular dynamics simulation and is more accurate and precise than the common histogram approach.