2003 Volkswagen Beetle

There could be a couple of reasons why that's happening the first one is the battery may have been low therefore the new alternator was charging it up, have you checked the water level? make sure you only use distilled water, and fill it to the bottom of the inverted cone, the other reason could be that you have a defective alternator and the internal regulator has malfunctioned charging the battery or should I say over charging the battery to the point that it is getting hot.