Substances which don't allow heat to easily pass through them are known as insulators. Insulators have crystal structure of molecules, molecules are far from each other, compared to conductors. Hence they cannot pass the heat easily through them, besides this insulators don't have free electrons to pass heat more quickly.
If needle is burnt then the heat transfer through the whole length of needle is faster because:
If needle is burnt then the heat transfer through the whole length of needle is faster, because needle (metal), being a good conductor of heat, heat passes along the whole length by conduction, in which heat is transferred by one atom to another connected atom quickly.