Melting is a transition where molecules that are structured within each other have that structure broken due to the heat.
Burning is a reaction that occurs within individual molecules, where the extra energy added causes the molecules to split and reform, typically consuming atmospheric oxygen as well.
Think of melting like taking apart legos and burning being like running legos through a blender.
*Edit* realized I’ve never answered the question…
If a thing has a chemical structure capable of burning, then whether or not it burns or melts depends on which one takes less energy to accomplish. However, you can bypass burning if you heat something up in an area deprived of oxygen.
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