The possibility that the apparent room temperature ferromagnetism, often measured in Co-doped ZnO, is due to uncompensated spins at the surface of wurtzite CoO nanoclusters is investigated by means of a combination of density functional theory and Mo
nte Carlo simulations. We find that the critical temperature extracted from the specific heat systematically drops as the cluster size is reduced, regardless of the particular cluster shape. Furthermore the presence of defects, in the form of missing magnetic sites, further reduces $T_mathrm{C}$. This suggests that even a spinodal decomposed phase is unlikely to sustain room temperature ferromagnetism in ZnO:Co.
