so yeah, i dont completely believe that wiki article. to me annealing makes total sense in how it effects materials... you raise the temperature thus allowing the atoms to move, then upon cooling they fall to a more stable configuration. lowering the temperature will only contract the material while cold. this still leaves the same structure (the same packing and electronic structure) when they are at room temperature just with less kinetic energy...
and as for when the materials were melted, bulk materials lose their magnetic properties at high temperatures such that when they cool the magnetic field aligns to any external field (an example is hot lava tracking the magnetic evolution of earth over millions of years... pretty cool really)... room temperature is plenty low in temperature that the packing of atoms wont rearrange, you just need to charge the magnetic field which is really just an electron thing... i just cant see why lowering the temperature would do anything since the nuclei are sort of besides the point... the electrons are what matter... right?
i guess there is no easy answer? but playing with LN2 is good fun...