Most of these comments imply that things only melt or burn depending on which thing happens first. That’s not the whole story though. Some materials simply don’t melt. In atmosphere they may burn, but if you take them into a vacuum with no oxygen available they still won’t melt.
IIRC all elemental materials have an associated phase diagram and will liquify under certain conditions. Molecular materials may or may not. In some cases they simply decompose into smaller molecules and/or sublimate away, if there is no oxidizer available to cause it to burn.
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