We apply the recently developed constrained-dynamics method to elucidate the thermodiffusion of vacancies in a single-component material. The derivation and assumptions used in the method are clearly explained. Next, the method is applied to compute the reduced heat of transport Q v* - h f v for vacancies in a single-component material. Results from simulations using three different Morse potentials, with one providing an approximate description of Au, and an embedded-atom model potential for Ni are presented. It is found that the reduced heat of transport Q v* - h f v may take either positive or negative values depending on the potential parameters and exhibits some dependence on temperature. It is also found that Q v* - h f v may be correlated with the activation entropy. The results are discussed in comparison with experimental and previous simulation results.