Melting Positive Battery Terminal

Stock OEM system has cable that bolt on not ones that go around. That's the first place I would check and then some continuity testing between the starter and the battery along with the rest of the starter cable system. Sounds to me like something is grounding out once you hit the start button. As you did not say the battery melted as soon as you turned the key on. That being said it points to the area I would be checking.
 
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