We have investigated the folding of polyalanine by combining discontinuous molecular dynamics simulation with our newly developed off-lattice intermediate-resolution protein model. The thermodynamics of a system containing a single Ac-KA(14)K-NH(2) molecule has been explored by using the replica exchange simulation method to map out the conformational transitions as a function of temperature. We have also explored the influence of solvent type on the folding process by varying the relative strength of the side-chain's hydrophobic interactions and backbone hydrogen bonding interactions. The peptide in our simulations tends to mimic real polyalanine in that it can exist in three distinct structural states: alpha-helix, beta-structures (including beta-hairpin and beta-sheet-like structures), and random coil, depending upon the solvent conditions. At low values of the hydrophobic interaction strength between nonpolar side-chains, the polyalanine peptide undergoes a relatively sharp transition between an alpha-helical conformation at low temperatures and a random-coil conformation at high temperatures. As the hydrophobic interaction strength increases, this transition shifts to higher temperatures. Increasing the hydrophobic interaction strength even further induces a second transition to a beta-hairpin, resulting in an alpha-helical conformation at low temperatures, a beta-hairpin at intermediate temperatures, and a random coil at high temperatures. At very high values of the hydrophobic interaction strength, polyalanines become beta-hairpins and beta-sheet-like structures at low temperatures and random coils at high temperatures. This study of the folding of a single polyalanine-based peptide sets the stage for a study of polyalanine aggregation in a forthcoming paper.