Here is a hot cut or a hot set, or a handled hot chisel.

This was made from a small 2 lb sledge hammer head. It was quite a chore to move the material by hand at the anvil, but I managed it well. I am quite pleased with how it turned out.

The point of a hot set is to be struck with a hammer. It is not a hammer itself, nor is it an axe. It is a chisel.
Such chisel is meant to be held over hot metal and struck by an extra person with a sledge to make the work easier.

It can be used by one operator, but only if the material to be cut is held down to the anvil or swage block.

Another way to use this tool by yourself is to have a hammer that swings itself for you. A treadle hammer, power hammer, etc.

Tools like this are usually called "top tools" the ones that are struck with a sledge.

They live a hard life being struck, and that means the handle breaks often and needs to be replaced regularly, or the striking surface gets worn down from being mushroomed over and another end needs to be forged welded on.

So, slipping on a simple handle like the one pictured is best for these kinds of tools.

It is not wedged on at all, and can be easily taken off.