If you are referring to the blue cone of a gas flame (eg Bunsen burner), then the part that is actually emitting the blue light is indeed the hottest as mibn2cweus says; but INSIDE the blue cone is the coldest part of the flame since that is where the gas/air mixture has not yet ignited.
Actually foolish the yellow flame is still very hot and burny (as you describe it). However, it is much more visible which is why it used as the "safety" flame.