The origin of spontaneous electric dipole moments and uncoupled magnetic moments, observed in niobium clusters below a size dependent critical temperature, are explained using first-principles electronic structure calculations. The calculated dipole moments for NbN (N=2-15) generally agree with the experiment and support the interpretation that the electric dipole has a structural origin. A strong correlation is found between structural asymmetry, as quantified by the inertial moments and charge deformation density and the electric dipole. For clusters with odd N, magnetocrystalline anisotropy is small in comparison to the rotational energy of the cluster, such that the spin magnetic moment (1 $\mu$B) is uncoupled to the cluster. Two potential mechanisms to explain the temperature dependence of the electric dipole are investigated. The excitation of harmonic vibrations is unable to explain the observed temperature dependence. However, classical simulations of the deflection of a cluster in a molecular beam show that thermal averaging reduces the asymmetry of the deflection profile at higher temperatures, which may affect the experimental observation of the electric dipole and polarizability. An experimental test is proposed to ascertain the importance of this effect. {\textcopyright} 2006 The American Physical Society.