Everything with a temperature above zero will radiate energy in the form of light, of a frequency determined by the temperature of the object. The higher the temperature of the object the higher the frequency of that radiated light. Most of the time that light is too low frequency for us to see, but things like snakes or thermal cameras can detect it. You can also sit near an appropriately named radiator and feel the radiated heat even if you can’t see it.
However as the temperature of an object increases the frequency of the emitted light can start to enter into our visible range and the object will start to glow. The candle flame’s color is determined by its temperature, which is why it is that yellow color. Everything of that temperature will be that color, even a tiny wire heated by electric resistance which is how incandescent light bulbs work.
You can look at the color temperature chart on light bulbs to see the the temperature required to produce the various colors of light.
There are other ways to produce unique flame colors such as introducing metals to the flames, but those are special cases.
The flame you see is basically just really hot smoke. Candle smoke is usually composed of wax. You can absolutely get a differently colored smoke if you add stuff like iron, sulphur or sodium. That’s how fireworks are made.
There’s also a blue flame, for example from a gas stove. That’s because gas doesn’t really produce ash particles. What you see is the energy being released from electrons
When things get hot they glow, and the colour they glow depends on the temperature.
Regular warm things only glow in infra-red so you need a special camera to see it. The soot particles (wax that didn’t burn all the way) in a candle flame glow yellow, like the sun.
Candles aren’t that efficient, so they have a lot of soot in to give the yellow colour. A gas burner, for example, has a better oxygen supply and cleaner fuel, so burns with very little soot and can be almost invisible.
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