Density functional theory calculations are used to compute the dipole polarizabilities of copper clusters. Structures for the clusters are taken from the literature for n=2-32 and several isomers are used for each cluster size for n≤10. The calculated polarizabilities are in good agreement with the prediction of a simple jellium model, but much smaller than experimental observations for n=9-32 [M. B. Knickelbein, J. Chem. Phys., 120, 10450 (2004)]. To investigate this difference, the calculated polarizabilities are tested for the effects of basis set, electron correlation, and equilibrium geometry for small-size clusters (n=2-10). These effects are too small to account for the theory-experiment gap. Temperature effects are also studied. Thermal expansion of the clusters leads to very small changes in polarizability. On the other hand, the presence of permanent dipoles in the clusters could account for the experimental observations if the rotational temperature of the clusters were sufficiently low. The potential importance of the cluster dipole moments implies that reliable ground-state structures and experimental temperatures are needed to find quantitative agreement between calculated and observed polarizabilities.