My doorbell stopped working. I tried replacing the transformer, but noticed it got very hot when I connected the wires that go to the chime.

I even bought a second transformer and it is also getting very hot.

The wires at the chime and to the door bell ringer are disconnected and hangling loose, so I know that there can't be a problem on that end.

Is it normal for a doorbell transformer to get hot? I am talking hot enough that I can't hold it. I am afraid of starting a fire.

What could be wrong?