In simple burners fueled by propane or oxygen, the blue flame will be hotter. However, blue flames aren’t always hotter than yellow flames, because the color of light emitted by the flame can depend on exactly which atoms and molecules are in the flame. Each atom or molecule has certain special frequencies (colors) at which it absorbs and emits light, just like a musical instrument has special frequencies at which it absorbs and emits sound. Sometimes that’s more important than the temperature of the flame in setting the color. Some chemicals burn with a blue color, for example, so that if you burn some of these on an ordinary fire it will look blue for a while (some fireplace logs may do this). This does not mean that the temperature of the whole fire went up, just that these chemicals made the color change.
I wouldn’t say blue flames are always necessarily hotter than a red or orange flame, though sometimes that is the case. Typically what determines the color of fire is what is being burned to create the flame. Blue flames are typical of burning gases like propane to cause a chemical reaction that results in said blue flame. Fireworks are the best example of this, in which different charges are treated with different chemical to get a desired color scheme. Most fires in the world burn with that yellow-orange color because they burn naturally occurring elements, like wood or oil.
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