Any solid existing in the universe possesses melting point. But practically, only pure solids can achieve its molten state. I'll tell you why.
Firstly, let us take an example of Iron rod. Consider a pure iron(or cast iron) rod. It will surely melt. This is because, the Iron molecules are confined intact with each other with a metallic bond. This metallic bond, in solids, is same as inter-molecular force of attraction. hence the temperature required to to break the metallic bond to melt it is same as the temperature required to break the inter-molecular force of attraction. Hence, the bond and the space molecules are broken at the same time.
Let us take another example of a Polythene bag. It is chemically a polymer of Ethylene (CH2=CH2). The Melting point of ethylene is 104.0K. But due to the polymer bonds, the melting point of polyethylene is amplified to 280K. The whole substance is uniform, the melting point of each monomer is same and hence the net melting point is same.
Now, let us take an example of wood. Wood is a mixture of Cellulose, Hemicellulose and Lignin majorly, and are composed of other different carbohydrates and proteins. The melting point of each compound is different and hence due to fractional distillation concept, the one that is more volatile will vaporize and then the less volatile one.
But, due to difference in bond structure, this doesn't happen. Instead, when wood is heated, it converts into CO2 and H2O. This is because, wood is basically confined of three bonds:- van der Waal's force; hydrogen bond; and covalent bond. And due to heat, vdW bond breaks first, and then H2 bond and finally covalent bond.
Wood can be melted only when all the three forces are equalized. This can be done only when the solid is compressed so that the "electronegativity difference-inter molecular force of attraction" between the atoms are equalized. This is practically not possible because, we require vacuum so that the combusting material does not react with oxygen or atmosphere air.
Hypothetically, this is possible but not practically.