The temporal stability of swept attachment-line boundary layer flow based on a swept Hiemenz flow model is studied. Starting from the global stability problem and motivated by analytical free-stream solutions, a Hermite expansion is employed in the chordwise coordinate direction which results in coupled local stability problems. A complete study of the temporal spectrum is presented and the discrete and continuous modes are classified according to their symmetry, chordwise polynomial order and asymptotic decay. Uniform, Görtler–Hämmerlin and higher-order modes are described in detail. Estimates are given for the location of the continuous spectrum, and bounds are derived for the validity of the linear approximation.