The colour of light depends on the wavelength of the photons. If something is hotter, the emitted photons have more energy and as a result a shorter wavelength. Blue has a shorter wavelength, whereas the wavelength of red is longer.
Flame colour is related to the energy not necessarily temperature. Blue light has a higher energy than red light. It is not guaranteed that the blue flame is hotter as there are other factors for example oxygen levels and what you are burning, that also determine the colour.
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