I believe that is a tested concept, if I'm not mistaken it is referred to
as an "adiabatic magnetic generator", or at least that seems very close...
The version that comes to mind is one where the magnetic domains are
aligned by a magnetic field and then the field is dropped, allowing the
magnetic domains in a soft iron core to 'randomly' rearrange themselves
according to environmental "thermal" noise. If I recall correctly that was
found to be a functional principle but output was extremely low compared
to relatively high input, although in a certain ideal situation it could
produce minimal amounts of power.
To do this with the curie point by heating it seems like an inefficient
way, seems to me more output could be derived from direct thermoelectric
effect... But I may be wrong of course.
But the main reason for there not being a magnetic battery is, in my opinion,
the fact that generation of current from a magnet needs active fluctuations of
the field intensity and/or polarity, so it needs to be an actively oscillating system,
and that falls in the category of electrodynamic generators while batteries
fall under the category of electrochemical reactors and need only contact surfaces
between different chemicals/elements to undergo reaction.
So it's a different type of beastie.
But in theory concepts such as "Bearden's" MEG should work, as should
variations on the concept. Basically, you can put a permanent magnet in
a transformer core exactly in the middle so half the flux goes around one
side of the core and the other half around the other side. Then you wrap
two small "primaries" or "controller coils" around the top or bottom "arms"
of the core, and two larger "secondaries" or "collector coils" around the
side "arms" of the core (where a normal core would have the primary and
secondary coils). Now you can feed alternating current to the "primaries"
in such a way that the flux from the central magnet is opposed by
one "primary" and in alignment with the other "primary", which guides
all of the magnets flux through the one leg of the core. At the moment
all the flux "flips" to that "leg" of the core, the "secondary" there will
"see" the flux in its core leg double in intensity, and it will generate a current.
Right after that, we alternate the polarity of the current through the "primaries",
and 100% of the magnets flux will now "flip" over to the other "leg".
This again induces a current in the "secondary" that has just lost all of the
flux in its "core leg", and at the same time it induces a current in the "secondary"
that suddenly "sees" all of the flux enter its formerly empty "leg".
And if we keep "flipping" the flux this way, we should be able to get output,
the power of which should be proportional to the strength of the permanent
magnets field and the frequency of oscillation.
Theoretically we should be able to get more out than we put in that way,
because it takes less energy to guide existing flux through one of two
flux paths of equal length than it takes to actually produce that same
amount of flux (like a normal transformer does, and there are already
transformers of the normal type that are 98% efficient...).
OU has been claimed for the MEG, but for some reason it is still not
available on the open market... It was said they had trouble closed-looping
the thing, but at the same time COPs of 300+% have been mentioned...