I think that insulated copper wire would do fine you just need to make sure that it is the correct diameter (too thin & it could burn out). I'm not sure what magnet wire is.
Magnet wire is supposed to be pure soft-drawn electrolytic copper which can only be used at moderately high temperatures, often copper-nickel is used for motor windings which have to stand higher working temperatures, for your purpose either would do, enamel coated of course.