Some science replies to various comments.
Example, heat a magnet and the field disappears or did it? The field may be weaker just simply because the force was sent further out over a
larger area and can no longer be detected. Cool it off, and presto, it returns.
This is a well-known phenomenon of ferromagnetic materials explainable with standard physics.
You have to consider that magnetism in materials is that way because of the alignment of the spins of electrons in the material: such spins generate
magnetic fields as an intrinsic property of the particle, i.e. there is no deeper explanation that we know about other than it is an observed fact
that electrons have a magnetic moment, period.
Ferromagnets (permanent magnets) have a special property that once you get some spins aligned, they tend to push their neighbors to be aligned in the
same direction. As a result you get whole large collections of atoms/electrons whose spins are all aligned and make a magnetic field. Most of the
time, they point every which way and so do not add up to anything macroscopic.
This is a thermodynamical process---as random motions from heat try to push the spins out of alignment and the self-attraction energy tries to bring
it back. So what happens is that at a certain temperature (Curie point) the heat is sufficient to tip the balance, and just like solids can melt at
a certain temperature, the permanent magnetism melts and the spins become unaligned, and the large scale field collapses. And yes, there is some
heat required to "melt" the alignment of the magnetic fields. This is a classic problem in statistical mechanics.
So the answer, "is the magnetic field completely gone" depends on how you think about it. The intrinsic generators of the magnetic field,
electrons, are still there, but now their individual fields are not aligned and so the outside field, feeling more than trillions of electrons is not
significant, because it feels the sum of the individual generators. But yet, the big external magnetic field really is gone.
Now, really cool it down, and the force falls in on itself and will do wierd things like superconducting.
Superconductivity doesn't happen with most materials---it is a very special, and very complex property. It is as if the quantum mechanicanical
nature, which is usually for tiny atoms, can self-interact and you get a macroscopic "quantum state". This is why it is so valuable and
fascinating. It has long been considered the only possible avenue into exploring quantum mechanics and gravity, as in the currently discussed
experiment. The reason is that because gravity is so enormously weak compared to other forces, and seeing the effects of quantum gravity would be a
tiny alteration of the already tiny force of classical gravity, you must have some kind of massive amplification of quantum mechanical properties
(superconductors) to even have a gnat's chance. Quantum gravity is so hard because the math is apparently intractable, and that we have very little
way of doing experiments. For other forces, we have particle accelerators, but the effect of gravity is so utterly insignificant with high-energy
particles comapred to the other huge forces. Then in the cosmos, there are astrophysical ways to probe gravity---but then you have such immense
sizes and masses that there is no significant influence of quantum mechanics any more.
There are various kinds of superconductivity, and apparently the newer "high-temperature" kind (liquid nitrogen versus liquid helium) did NOT show
any novel gravitational effects. This is probably because the quantum mechanical properties of the higher-temperature class of superconductors are
distinct from the older class.
Kind of a bummer, as liquid helium experiments are much harder and more expensive than liquid nitrogen experiments.