Why does methane burn colorless?

The color of the flame depends on the elemental composition of the material to be heated and the temperature at which it is heated. This is due to the fact that heat brings the electrons in the element into an excited state; when these electrons return to the ground state, visible light is often emitted.

There is not much carbon in methane. Consequently, burning methane does not get as hot and its flames will not be the same color as materials that burn more exothermically and lead to higher temperatures.