What determines whether something melts or chars/ignites when heated?
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If it can react rapidly with oxygen at the temperatures it’s being heated to then it’s going to ignite. If not then not.
It depends on how stable the chemical is.
Things that melt remain the same thing as they heat up. Often times, this is because they’re a single element (see: any metal), but also applies to stable compounds (water, for example).
If the compound isn’t stable, it breaks down as it heats up. For example, carbohydrates, even in the absence of anything else, will break down into carbon and water as it heats up. This is charring – “charring” usually specifically involves carbon being left behind; but the same kind of thing can happen even without carbon. For example, heating rust results in pure iron.
Ignition specifically requires a chemical reaction that releases more heat – and often requires access to oxygen or some other thing for the chemical to react with. It’s like charring, except that charring is usually just things breaking down and falling apart, while ignition is things breaking down in a way that releases energy.
Typically it’s a comparison between its melting (or boiling) point and the temperature at which am oxidation reaction becomes self sustaining. These reactions produce net energy, often, but also require a threshold to initiate, referred to as the “activation energy”. In order for a reaction to be self sustaining, the energy released must bring at least one other molecule of the substance over the activation energy threshold. If the nearby air is too cold, for instance, too little of the emitted energy will be absorbed by the adjacent reactants to ignite them, and so the reaction fizzles out.
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