When an object, such as a lump of iron, is accelerated by a magnetic field, where does the extra kinetic energy come from? Does the object become colder, or is it demagnetized?
If the iron accelerates as the result of an electromagnet being turned on, then the answer is obvious: the energy is supplied by the magnet power supply. If the iron is restrained and then let go, the kinetic energy is converted from the potential energy of the separated system. That is, it took energy to separate the iron and magnet in the first place and to keep them separated.
A magnetic field has an energy density which is proportional to the square of the field. A ferromagnetic material has small magnetic domains which align so as to reduce the external field. The KE comes from the reduction of the field's energy density.