For molecular nanomagnets, excesses of magnetic entropy at finite low temperatures are induced by degrees of freedom resulting from macroscopic degeneracies of the molecular spin states. We experimentally demonstrate that this effect can be huge and efficiently exploited for enhancing the magnetic field dependence of the adiabatic temperature change. We specifically consider the Mn32 molecular nanomagnet, proving it to be an excellent magnetic refrigerant below T≈2 K, due almost entirely to its spin degeneracy.