The translational motion of molecular ions can be effectively cooled
sympathetically to temperatures below 100 mK in ion traps through Coulomb
interactions with laser-cooled atomic ions. The distribution of internal
rovibrational states, however, gets in thermal equilibrium with the typically
much higher temperature of the environment within tens of seconds. We consider
a concept for rotational cooling of such internally hot, but translationally
cold heteronuclear diatomic molecular ions. The scheme relies on a combination
of optical pumping from a few specific rotational levels into a ``dark state''
with redistribution of rotational populations mediated by blackbody radiation.Comment: 4 pages, 5 figure