We have considered the question of whether the Hubbard Hamiltonian can lead to properties characteristic of two types of semiconductors, depending on the value of the ratio &Dgr;/Iof bandwidth to intra‐atomic Coulomb integral. In one type there is a transformation, with increasingT, from a magnetic insulating state to a paramagnetic insulating state, and in the other the system goes from a magnetic insulating state to a paramagnetic metallic state. We have applied a new variational single‐determinantal approximation which, in contrast to the standard thermal Hartree‐Fock approximation, duplicates the exact behavior of the model both in the atomic limit, &Dgr;/I=0, and the band limit &Dgr;/I=∞. Limiting ourselves to well‐known types of one‐electron states, we have obtained stability boundaries (as determined by the free energy) between various phases. While the boundaries obtained to date have intrinsic interest, we find that further calculations are necessary to completely answer the question raised above.