Cost for a new alternator versus a rebuilt, plus installation

We don't know. Take the alternator and have it tested. What made it overheat? Is the drive belt still on the engine? If not,that will make it overheat and your battery will be drained! cost for a new or reman alternator depends on the engine size,which was not included in your question. best price on parts,new or reman is at rockauto.com