To my understanding, the magnetic properties in iron and other materials rely more on
- The crystal structure in the material being aligned in a certain way. Cooling your heated iron inside a magnetic field will align it to the field and retain that alignment once cooled (hence making it a permanent magnet). Or as in your example, break a previously strong alignment if the new magnetic field in which it cools is comparably weak, i.e. the earth's magnetic field. (Stroking an object repeatedly with a permanent magnet might also tend to align crystals, although the final effect will be much weaker.) Also, striking an object (with e.g. a hammer) can also weaken an alignment of the crystal structure.
- Some materials conduct magnetic field lines better than other materials (e.g. laminated transformer core vs. air), even if not especially aligned.
Of course, not all iron-containing materials are equal. In the old folklore days one might have had much less choice between different alloys, but these days a lot of advances have been made in the metallurgy science.
Manipulating objects (that have at least some iron content, e.g. nails) via controlling magnetic fields (perhaps induced via strong electrical currents in the brain) must seem like magic (google levitating magnets). These could conceivably be deflected via other ferromagnetic objects... I wonder if nerve tissue would really be able to withstand such quite powerful electrical surges... Maybe only certain people having such a very rare genetic trait, which may be passed on to offspring.
Such an explanation would severely limit the kinds of "magic" possible, much less than what one reads about in fantasy novels. Then again, the folklore of old may have tended to exaggerate especially after some generations of oral transmission.
Seems you are venturing into Magneto territory.