We study the unbiased folding/unfolding thermodynamics of the Trp-cage miniprotein using detailed molecular dynamics simulations of an all-atom model of the protein in explicit solvent using the Amberff99SB force field. Replica-exchange molecular dynamics simulations are used to sample the protein ensembles over a broad range of temperatures covering the folded and unfolded states at two densities. The obtained ensembles are shown to reach equilibrium in the 1 mus/replica timescale. The total simulation time used in the calculations exceeds 100 mus. Ensemble averages of the fraction folded, pressure, and energy differences between the folded and unfolded states as a function of temperature are used to model the free energy of the folding transition, DeltaG(P, T), over the whole region of temperatures and pressures sampled in the simulations. The DeltaG(P, T) diagram describes an ellipse over the range of temperatures and pressures sampled, predicting that the system can undergo pressure-induced unfolding and cold denaturation at low temperatures and high pressures, and unfolding at low pressures and high temperatures. The calculated free energy function exhibits remarkably good agreement with the experimental folding transition temperature (T(f) = 321 K), free energy, and specific heat changes. However, changes in enthalpy and entropy are significantly different than the experimental values. We speculate that these differences may be due to the simplicity of the semiempirical force field used in the simulations and that more elaborate force fields may be required to describe appropriately the thermodynamics of proteins.