We combine first-principles calculations and Boltzmann transport theory to study the thermoelectric properties of intermetallic compound YbAl 3 . To accurately predict the electronic relaxation time, we use the density functional perturbation theory and Wannier interpolation techniques which can effectively treat the electron-phonon scattering. Our calculated transport coefficients of YbAl 3 are in reasonable agreement with the experimentally measured results. Strikingly, we discover that in evaluating the Seebeck coefficient of YbAl 3 , the scattering term has a larger contribution than the band term and thus should be explicitly considered in the calculations, especially for the case with localized bands near the Fermi level. Moreover, we demonstrate that by reducing the sample size to less than ∼30 nm, the electronic thermal conductivity of YbAl 3 can be sufficiently suppressed so that the thermoelectric figure of merit can be further enhanced. [ABSTRACT FROM AUTHOR]