We calculate the magnetic dipole and electric quadrupole moments associated with the radiative Omega(Q)* -> Omega(Q)gamma and Xi(Q)* -> Xi(Q)'gamma transitions with Q = b or c in the framework of light cone QCD sum rules. It is found that the corresponding quadrupole moments are negligibly small, while the magnetic dipole moments are considerably large. A comparison of the results of the considered multi-pole moments as well as corresponding decay widths with the predictions of the vector dominance model is performed.