I know the properties of a permanent magnet change with temperature and that different magnetic materials have different temperature coefficients. If a permanent magnet has a temperature gradient across its length (i.e one end of the magnet is at a different temperature to the other), which temperature will the properties of the magnet correspond to? Will it act as if the entire temperature is the same as the lowest temperature end, the highest temperature end, or something in between (the mean temperature perhaps?)? Or is it more complex than being able to estimate its properties to a single temperature?
The simplest answer is "something in between". Your problem is more complex, as you expect. There is no ready formula that you could use in this case. You can imagine the final result as if your magnet with temp gradient was the series of thin slices of a magnet, but each slice had different properties. Assuming that you know the property vs. temperature, you can build such set of slices and determine the property of the whole set. As the first step you can use any simple FEM software, build the mesh, apply the respective properties to each cell/slice and do the calculation.
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