I know that heat is the particles in a substance vibrating randomly, and that a magnet has some kind of effect on magnetic materials that makes all the particles act in unison. I realize that this is a long shot, but is there a way to align the particles of a magnetic material with a magnet such that when the material gets hot the whole object vibrates?
no. There is no reason for any vibration to occur, even magnet to magnet.
I dont think of it would warmth as much as boot. If the iron rod have been electrically insulated as you're saying then there would be no cutting-edge bypass. you merely have an electrically polarized iron tube. the only source of warmth would be from the friction with the magnet and the non-magnetic rod /air and so on.
no, the individual parts (magnetic domains) would vibrate but not the whole piece. Heating demagnetises iron. To make a magnet vibrate you need a changing magnetic field, that's how loudspeakers work, the coil is inside a permanent magnet, and you pass an alternating current in the (electromagnetic) coil so it is attracted, then repelled by the permanent magnet. Old-fashioned electric bells work by breaking the circuit to the electromagnet so that every time it moves, you cut off the power so it is pulled back to it's original position and the contact is made again, this makes it vibrate too. But not heat.
