Yeah... you're going to have to relax your requirements. An air cored winding gets very hot indeed, very quickly indeed, making 1.5T!
What size magnet are you using? N50 is the grade, it tells us nothing about the size, shape or energy of the thing.
Exactly how big of a magnetic field do you
really need? Technically the dipole moment is what you're after: you're trying to make a magnetic stirbar spin, and the flux density required to do this doesn't really matter, just that it gets enough moment to pull it around.
Typical planar and flat coils will do fine in the 10mT range, which is enough to spin, like, something in a flat or round bottomed flask I suppose, in a not very viscous fluid, at a modest speed.
Do you know how much torque you need for a given stir rate and viscosity?
Nevermind granular or lump materials, maybe you can approximate an average or worst case viscosity for that?...
It would be nice if there were a way to gear down a stirbar, so that for example a pile of small ones could spin very fast (which won't need much flux density). Alas, fluid dynamics just doesn't work that way...
The point of that being, magnetic fields are relatively weak, at least fields that we can create easily. But we can vary them extremely quickly, equivalent of millions of RPM in this sort of arrangement. So while the torque may be feeble, we can compensate by cranking RPM up, and power is proportional to both. That's why small motors are so fast and loud, and why gearboxes are so necessary to make use of them. You lose this advantage in direct-drive applications, which usually results in ugly compromises, like really wide hub-shaped motors -- the large hub means more magnetic field area to get the torque needed.
BTW, the limiting factor is literally just copper -- if we had an about 10 times better conductor, we'd be sitting pretty good actually, with applications like this. Well, your hotplate and any surrounding metal might not be so happy (being pulled/pushed/spun by the fields, and heated up by induced currents unless made of the same mythical metal), but the core idea would work. We can actually do even better than that, in fact infinitely so -- but only at low temperatures, where superconduction becomes possible. Go figure, eh?
Tim