AC to DC power supply questions
Yes, the 7812 is overheating and should be shutting down. The +28V input is way too high and creating too much heat. A 24V center-tapped transformer will produce a rectified and filtered 16v which will be fine if your electricity does not have brownouts.

The datasheet for the 7812 shows its thermal resistance and finned aluminum heatsink manufacturers show how much heat they remove.