No, it's not really a form of energy (in some sense, anyway).
All materials are made from atoms, which themselves include electrons whizzing round in orbits (a simplified view, but it'll suffice). Each electron is in effect a little magnet.
In most materials, there are enough electrons and atoms, in enough random configurations, that they cancel out their overall magnetic properties.
Some materials are susceptible to an external magnetic field, so that under a magnetic field all their electron spins align to a certain direction, turning into a magnet. This is a paramagnet.
Some materials stay aligned like this even without an external magnetic field (such as your magnet, whatever material it may be). This is a ferromagnet.
Now, are you aware that heat is simply the amount of jiggling energy that something does? If you jiggle a lot, you'll get warm (why we shiver in the cold, for example). Same with atoms too.
But, this material that stays magnetic without an external source of magnetic field, like your magnet, is like that because all the spins align, as I said above. But applying heat to this will make them jiggle and go random, which means that their spins with become randomly aligned, and they'll no longer be a magnet (as explained above too).
So, to remove the magnetic properties, you can simply heat the material.
In the absence of heat or external magnetic field to remove the magnetic properties, your magnetic will stay like that.