Diamonds' molecular structure is such that when one melts, it transforms into something else, so that what melts is no longer a diamond.
Another Answer
Diamond mineral has the highest melting point of any mineral: 3,820 degrees Kelvin.* Once melted, the above answer is correct: it's no longer the diamond that you're familiar with and can never be reconstituted as such.
*3,547º C. or 6,416.6º F.
Diamond
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When something melts it turns into a liquid
What can happen when the glacier melts in a cirque
It forms a liquid! Gallium the metal that melts in your hand!
It melts !
it melts
it melts
brine
it melts
When a candle melts it gradually loses its shape, and turns into a puddle.
... it melts... and becomes part of the ocean.