A previously developed theory of the magnetism of iron, based upon the notion of a randomized exchange field, is modified and extended. It is shown that Coulomb fields arise in association with the randomized exchange field; the modification allows one to take into account these fields, which are found to change the details of the previous results without affecting the main conclusions. The theory has been extended to calculate the properties of the model at finite temperatures: the Curie temperature (1840 K), the magnetization curve, the paramagnetic susceptibility (a Curie-Weiss law), and the effective interatomic exchange coupling are calculated for iron. The magnitudes of the atomic spin moments were found to vary little up to 1.5 times the Curie temperature. © 1979 The American Physical Society.