From magnetic circular dichroism measurements of the Heusler alloy NiMnSb, in combination with other techniques, we show that a dramatic increase in the Mn and Ni moments occurs below a "crossover" transition temperature of about 80-100 K. This phase transition is well below the Curie temperature of NiMnSb (similar to 730 K). While the spin polarization near the Fermi level, from spin-polarized inverse photoemission, remains very high for k(parallel to) = 0, it is unlikely that NiMnSb is a half-metallic ferromagnet near room temperature.