A: Yes, the neodymium magnet will lose its magnetism when heated above its Curie point. Unless it's held in a strong field while it's cooling, however, the magnetic directions of those little domains will point all different directions. Their fields will mostly cancel, so it won't act like much of a magnet any more.
What would happen if you melt a magnet?
High temperature destroys this ordering and therefore destroys permanent magnets, the temperature at which ferromagnetism is lost is called Curie temperature, and is below melting point of the material. Thus a magnet will lose its magnetism before it melts.
Are magnets stronger hot or cold?
In extremely cold temperatures the atoms will move more slowly and less randomly. This creates a more controlled alignment of the atoms that produce the magnetic field and a slightly stronger magnetism.