Computer simulations are increasingly being used to predict thermodynamic observables for folding small proteins. Key to continued progress in this area is the development of algorithms that accelerate conformational sampling. Temperature-based replica exchange (ReX) is a commonly used protocol whereby simulations at several temperatures are simultaneously performed and temperatures are exchanged between simulations via a Metropolis criterion. Another method, self-guided Langevin dynamics (SGLD), expedites conformational sampling by accelerating low-frequency, large-scale motions through the addition of an ad hoc momentum memory term. In this work, we combined these two complementary techniques and compared the results against conventional ReX formulations of molecular dynamics (MD) and Langevin dynamics (LD) simulations for the prediction of thermodynamic folding observables of the Trp-cage mini-protein. All simulations were performed with CHARMM using the PARAM22+CMAP force field and the generalized Born molecular volume implicit solvent model. While SGLD-ReX does not fold up the protein significantly faster than the two conventional ReX approaches, there is some evidence that the method improves sampling convergence by reducing topological folding barriers between energetically similar near-native states. Unlike MD-ReX and LD-ReX, SGLD-ReX predicts melting temperatures, heat capacity curves, and folding free energies that are closer in agreement to the experimental observations. However, this favorable result may be due to distortions of the relative free energies of the folded and unfolded conformational basins caused by the ad hoc force term in the SGLD model.