Melting and burning are actually quite different processes; melting is an example of a physical change while burning is an example of a chemical change. Most materials have high melting point. Combustion temperature determines when the material will burn.
The energy required to start the reaction (called the energy of activation) determines whether the material will melt or burn. This energy is in form of temperature or other conditions like oxygen availibilty etc. For some materials, the melting point is much higher than the combustion temperature, hence they burn before they can melt.