Will molten iron stick to a magnet? I've known for a long time that if you heat a magnet, there is a point it loses its magnetism (the Curie temperature).  It isn't clear to me if this applies to induced magnetism like iron sticking to a magnet.
Will molten iron behave like a ferrofluid and be attracted to a magnet or will it just have a very weak paramagnetic attraction?
 A: The loss of magnetism at the Curie temperature applies primarily to "induced magnetism like iron sticking to a magnet". 
Ferrofluid doesn't really include a molten iron; ferrofluid is a collection of many small but mezoscopic particles, "sawdust", and its magnetism doesn't differ so much from magnetism of normal pieces of iron except that it's easier for the particles to change the orientation. Ferrofluid normally have lots of "normal fluid" in it, like water or organic liquids, and some "coating", so the ferromagnetic material is a relatively minor component and it's surely not melted.
When a ferrofluid gets heated to the Curie temperature, it loses its magnetism, too.
The Curie temperature of all sensible materials is and has to be below the melting point. When you approach the melting point while heating the material, the magnetism has been lost for quite some time.
Yes, molten iron is paramagnetic, much like every ferromagnetic material above the Curie temperature.
A: If the metal heats up the magnet above around $500^\circ\mathrm F$ the magnet will lose it magnetic characteristics, and will not regain those properties when it cools down. 
