Structural and magnetic properties of finemet under various heating conditions, but always without magnetic field, were investigated. Rapid nanocrystallization took place near below 773K and the amorphous fraction of the fully transformed sample was about 30%. The final state was not sensitive to the heating rate but depended on the maximum temperature. \mu\(max) was 760.000 at 50Hz exiting field and the DC permeability was over 1.200.000, which is the largest permeability published in literature for heating in absence of magnetic field. On the basis of this result, preparation of materials with such large permeabilities and with magnetic properties insensitive to temperature and mechanical conditions is possible.