Shielding-current-induced fields (SCIFs) in magnets wound with coated conductors deteriorate the field quality of the magnets. Particularly, in magnets that are excited repeatedly, and must generate time-varying magnetic fields, for example, in certain types of accelerator magnets, the influence of the temporal behavior of the SCIFs on magnetic field is quite complicated. We focused on the magnetic field drifts and conducted magnetic field measurements using a small dipole magnet wound with coated conductors cooled using a cryocooler. The magnet was operated under various patterns of excitation, and magnetic fields were measured using a rotating pickup coil, which enabled us to measure the dipole and sextupole components of the magnetic field. Numerical electromagnetic field analyses were conducted to examine the current distributions in conductors, which influenced the temporal behavior of the magnetic field.