  Dust grains coagulate into larger aggregates in dense gas. This changes their
size distribution and possibly affects the thermal evolution of star-forming
clouds. We here investigate dust coagulation in collapsing pre-stellar cores
with different metallicities by considering the thermal motions of grains. We
show that coagulation does occur even at low metallicity $\sim 10^{-6} \Zsun$.
However, we also find (i) that the H$_2$ formation rate on dust grains is
reduced only after the majority of H$_2$ is formed; and (ii) that the dust
opacity is modified only after the core becomes optically thick. Therefore, we
conclude that the effects of dust coagulation can safely be neglected in
discussing the temperature evolution of the pre-stellar cores for any
metallicity as long as the grain motions are thermal.
