[en] Laser cooling of ion beams generally operates only upon the longitudinal motion of an ion beam. In order to extend this powerful dissipative force to the transverse directions, we consider introducing a Wien filter in a cooing straight section. It is theoretically shown that longitudinal cooling within a Wien filter naturally develops a transverse (mostly horizontal) cooling effect as well. Molecular dynamics simulations demonstrate that this method enables us to reach an ultralow-temperature state of a stored ion beam. (author)