It is my understanding, from reading the statute, that the melting down with the intent to sell the altered coin makes it illegal.
From Title 18 United States Code, Section 331:
"Whoever fraudulently possesses, passes, utters, publishes, or sells,or attempts to pass, utter, publish, or sell, or brings into the United States, any such coin, knowing the same to be altered, defaced, mutilated, impaired, diminished, falsified, scaled, or lightened"