In most diamagnetic substances the strength of dipolar interactions between nuclear spins is such that temperatures of the order of a microdegree or less must be obtained for cooperative effects to take place. Rather than cooling the whole sample we have cooled directly the nuclear spins of19F in CaF2, which are thermally isolated for the duration of the experiment by the weakness of the spin‐lattice relaxation mechanism. The cooling takes place in two steps. First, the spins are polarized in a high field by the ``solid effect'' to an equivalent temperature of the order of 5 mdeg. Second, they are demagnetized in the rotating frame reaching a temperature below one microdegree. For negative temperatures their transverse susceptibility as a function of initial polarization exhibits a plateau characteristic of antiferromagnetic behavior. Results are in qualitative agreement with a molecular field theory.