Most likely you are thinking of the yellow in the flame. This comes from very fine soot particles that glow with black body radiation. So these are actually particles, not just heat, though the heat (more specifically the temperature) is necessary to cause glowing.
Other colors, like blue, are from molecules transitioning between states (e.g. circumstances cause two oscillating atoms to change how quickly they are oscillating, or maybe two bonded atoms break apart), and so the change in energy between the two states causes a release of energy in the form of light (conservation of energy). The energy is proportional to the frequency.
So, the flames that we see coming from fire is not actually heat. They are the burning matter, a source which produces heat.