We present the calculation of dynamic properties of the hyaluronan oligomer (UA)(4) based on the second-order solution of the diffusion equation in the Smoluchowski limit. The equilibrium averages necessary for the solution are calculated from replica-exchange Monte Carlo simulations in implicit water models. This simulation technique was shown to avoid the trapping of the configurations in local minima typical of simulations in the canonical statistical ensemble. A simple implicit solvent model was applied to (UA)(4) taking into account the hydrophobic effect in water solution and hydrophilic local effects due to efficient hydrogen bonds with the solvent. The correction of the statistics due to a finite difference solution of the Poisson equation, not directly included in the simulation, was included through a perturbative method. Several configurational distributions and dynamical parameters related to nuclear magnetic relaxation, sensitive both to the molecular structure and to mobility, were calculated from the replica-exchange Monte Carlo statistics at different temperatures. These data compare fairly well with experiments and with the results obtained by standard molecular dynamics simulation in the explicit water solvent and in the canonical ensemble at T = 300 K. Implications in the macromolecular dynamics of hyaluronan were discussed.