The thermodynamic properties of a 46-mer b-barrel protein model are investigated using Langevin dynamics and the histogram analysis method. By obtaining the density of states distribution and using the methods of statistical mechanics, we are able to identify the thermodynamic transitions for this model protein and characterize the nature of these transitions. Consistent with an earlier study of this model, we find that the transition from a random coil state to a manifold of collapsed but nonnative states is a continuous transition, and the transition from the manifold of collapsed states to the native state is first order-like. However, our calculations indicate that the folding transition is only weakly first order. Most importantly, we are able to characterize the free energy surface of the protein model, as well as the processes of compaction and native structure formation, from a statistical point of view. We also examined the thermodynamic transition state. By combining the earlier kinetic analysis for the same protein model, we provide a more complete description of this model protein and propose possible further modifications of the model to improve its stability and foldability.