Accurate usually means "true to the original" the original being whatever is fed to it as noted above.
OTOH, "warm" can be one or more of many things: a BBC type downward sloping speaker response curve, linear or non-linear distortion, muted high frequencies, augmented mid-bass frequencies, over-damped listening room, blown tweeter ;), a recording without strident highs, a well-balanced recording, lack of sibilance and very extended high frequencies...
OTOH, "warm" can be one or more of many things: a BBC type downward sloping speaker response curve, linear or non-linear distortion, muted high frequencies, augmented mid-bass frequencies, over-damped listening room, blown tweeter ;), a recording without strident highs, a well-balanced recording, lack of sibilance and very extended high frequencies...