Doorbell transformer is getting hot when I replaced it and doorbell still isn't working

Jason, you may have a short circuit. That would cause the transformer to get hot...
You will need to use an electrical meter with a setting for testing circuit resistance.
Do you have any electrical knowledge?

Transformers typically get warm. However, are you sure you have primary and secondary wired properly? Did you check the continuity at the pushbutton? If this is an old doorbell system are the plungers free?