In some paramagnetic media, the effective field Hi, which includes an effective exchange field and an applied field, can cause a splitting of the ground level. In the temperature region T>Tc (Tc is the Curie temperature), there are certain probability distributions of electrons on two energy levels due to ground-state splitting. This induces the ground level for a double transition. It is shown that there are several temperature behaviors for the magneto-optical Faraday effect in paramagnetic media. If the applied field is not too large, the ratio of the Verdet constant to the magnetic susceptibility is V/x=A (1+BT) in some media, or V/x=A (1+B/T) in other media. It is also indicated that both the real part θ' and imaginary part θ" of the Faraday rotation are proportional to the effective field Hl, and show similar temperature behaviors beyond the region of optical absorption.