Heat has nothing to do with electricity or magnetism... And yet heat carried through electromagnetism is why life on Earth exists, and by extension, why you're able to tell me here and now that they have nothing to do with each other. It's just a little ironic. Heat can be transported by radiation, and the magnetism can deflect/repell radiation, and therefore, heat. But you are right in that magnetism can't contain pure, raw heat. However, the fact that magnetism can affect sources that generate heat means you're right on a technicality.