80°C is the Curie temperature for neodymium magnets, (the temp magnets de magnetize), for ferrite is a couple hundred degrees celsius, and some hi temp magnets can hold arround 800°celsius

Would piezo electric crystals or molecularly aligned crystals be able to conduct magnetism and help put some distance between a cheap neodymium or AlNiCo magnet, so it can still generate without de-magnetizing from the heat?

If you're not using electro you could protect the magnets with something like starlite.

⁠@@gerryplayz4532starlite is just highly pourous carbon, and will burn away just like other forms of porous carbon (think charcoal) when exposed to sufficient air and heat - which a rocketstove flame path definitely provides.

As in, the moving magnet is attracted to another magnet above it, heat makes it lose it's attraction and fall into a colder area below it, the cold causes it to regain it's attraction and go up again, and in that way a temperature difference causes up-and-down motion? I don't know if that would work or not, or if that's even what you meant. It's just something that popped into my head just now.

And that wire that responds to heat would be perfect to try and include for such a motor.

You're asking about the difference between magnetic field strength B (units Tesla/T) and magnetic flux Φ (units Weber/Wb). The density of magnetic flux basically equals the field strength. 1 T = 1 Wb / m^2. In a motor or electromagnet, the field strength at the center of a coil is, indeed, inversely proportional to the radius (there's a factor of 1/r) : B = (μ0 I/(2R))n, where μ0 is the permeability of free space constant, I is current, R is radius, and n is the dipole vector (the direction the coil faces, your thumb in the right hand rule). For any given constant current in a loop of wire, there will be a constant amount of magnetic flux inside that coil. A larger radius spreads out that flux over a larger area, thus resulting in a weaker field at any given point. In a generator, however, current depends on the load (and torque), and we have a different equation for determining voltage. For a straight length of wire, E=Blv sinθ, where E is voltage, l is the length of wire, v is the velocity, and θ is the angle that the wire cuts the magnetic field lines. Of course coils are made of wire, so we could do an integral to figure that out, but we have a shortcut. For coils of wire, the Faraday-Lenz law describes the voltage as E = -N dΦ/dt , that's the number of turns times change in magnetic flux over time. Note that radius is not present in that equation. It is governed entirely by the magnetic flux passing through the area of the coil. All that is to say, you can have a very large radius and still get the same voltage out of a magnet, as long as it's not so large that the magnetic field starts turning backwards within the coil. You can use metal or ferrite field guides to help with that. AC clamp-on amp meters rely on this fact. The real limit on radius is how many coils you can fit in the armature, and how big the radius of the rotor needs to be. The width of the coil is, to my mind, a bigger factor, because you're getting farther away from the magnet. Again, if you guide the field to go straight down the whole width of the coil, that's fine, but in open air you would start losing field rapidly the farther away you get, proportional to 1/r^3.

Use a metal ion solution that will evaporate to cool magnets

@@dylaninnes8541 perhaps, and my initial idea was a hollow channel or tubing in the magnet with coolant going through it.

@@ForeverLoveCats yeah if it was a closed system

MHD generators are being used to recover some waste energy in coal burning plants, raising their efficiency. So, power companies do use an advanced and refined version of this.