From what I can tell only certain materials appear as ferromagnets or antiferromagnets (which one depends on their exchange interactions). For these materials if risen above a certain temperature, the Currie temperature in the case of ferro and Neel in the case of antiferro, they lose their ordered magnetic properties and become paramagnets.
This is to do with the strength of the thermal fluctuations. If we take an arbitrary material (e.g. Cu or Si) I would except what when dropped below a low enough temperature they would start the see these ordering effects due to interactions. Is this the case? i.e can any material be made into a (anti)ferromagnet at low enough temperatures? Is so why and if not why not?