A novel combination of replica exchange Monte Carlo sampling techniques with a histogram analysis approach is developed and applied to study the thermodynamics of the folding transition in a face-centered cubic lattice chain protein model. Sequences of hydrophobic (H) and polar (P) topology residues were designed to fold into various beta -barrel type proteins. The interaction scheme includes the short-range propensity to form extended conformations, residue-dependent long-range contact potentials, and orientation-dependent hydrogen bonds. Weakly cooperative folding transitions could be observed for properly designed HP. (Hydrophobic and polar residue sequences with cooperative long-range interaction methods were proposed and tested.) Based on the study of these systems, the computational cost of such an approach is many times less than the cost of other Monte Carlo procedures. This opens up the possibility for efficient studies of the folding thermodynamics of more detailed protein models.