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This isn't necessarily true. It depends on WHY the flame is blue.

However, it is true that in order for black body radiation (aka cavity radiation) to appear blue, the object it's coming from must be significantly hotter than an object from which the cavity radiation appears red.

Blue light has a shorter wavelength (and therefore a higher energy) than red light, so it requires a hotter object for the blue wavelengths to predominate.

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