A light is burning

Unfortunately, your answer is wrong.

Take a close look at it again. The wax starts to melt.

The heat is strong enough hto change the aggregate state of the wax - it changes from solid to liquid. If you would heat up the liquid wax a bit more, it would evaporate. This evaporated wax burns. This fire is the flame of the candle.
The wick burns because it is wrapped in wax which evaporates very quickly. Therefore, it is important for a candle to have a sufficient amount of wax to evaporate.