Q:

Melting Point of Amorphous Solids

My textbook says that amorphous solids do not melt at a fixed temperature,but at a range of temperature. It depends on the way the atoms/molecules are present in a given piece  of solid. 

Since the melting point(range) depends on the whole solid piece , can it be said that melting point of amorphous solid is an extensive property?

A:

No matter how the structure is the heat given to the substance will be distributed over many molecule/ atoms. And the all molecules will more or less the average energy. So, on average temperature will be same across the substance. This will happen even if the substance does not conduct heat well but on a smaller region.
For breaking a bond, you need specific amount of energy. Boiling or melting needs a lot of bonds to be broken. Most molecules, on average will gain that energy on a specific temperature.
So, that being said, the m.p. and b.p are not extensive properties. Being amorphous or crystalline doesn't change the reasoning.

