During periods of northward IMF, plasma sheet ions often have two components: hot (magnetospheric origin) and cold (magnetosheath origin). The temperatures of the cold-component ions are ~30--40% higher in the dawn sector compared to the dusk sector, implying the dawnside magnetosheath ion heating of ~30--40%. As a result, the magnetosheath ions are less distinguishable from the hot-component ions, which have lower temperatures on the dawnside, leading to a higher occurrence of the ions having (apparent) one-component distribution. As the duration of the hourly averaged IMF being northward (Δt) increases from 1 to 10 hours, the occurrence of two-component ions increases from 65% to 83% in the dusk flank, but in the dawn flank it remains relatively stable at around 45%. In contrast, the occurrence of ions best characterized by kappa ($kappa$) distribution increases from 25% to 35% in the dawn flank whereas in the dusk flank it remains relatively insensitive to Δt (10%). The occurrence of a one-component Maxwellian distribution appears to be most pronounced in the region of the plasma sheet close to the midnight meridian, and these ions appear to be characteristic of the nominal plasma sheet (hot component) ions. The densification of the plasma sheet, as Δt increases, mainly results from the influx of the magnetosheath ions. However, the cooling of the plasma sheet ions can be attributed not only to the influx of the cold magnetosheath ions but also to the cooling of the nominal plasma sheet ions. The dawn-dusk asymmetries observed in the cold magnetosheath ion profiles should provide constraints that can help determine the roles of various proposed magnetosheath ion entry mechanisms.