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240 C 

One reason that you might not find a boiling point is that the styrofoam might break down ( decompose ) so that bonds break WITHIN the chain of the molecules before all the forces between the chains break ( so that it would boil ).

Another reason is that the chains are all different lengths and so different masses. This may mean that the styrofoam may melt over a range of temperatures. 

Boiling is when a compound turns from a liquid into a gas. As polystyrene is a polymer it contains very large molecules which would require a lot of energy to separate and turn into a gas so the boiling point would theoretically be incredibly high. But at this high temperature the chains themselves would have broken down so polystyrene doesn't have a boiling point only a melting point. 

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