When two wires touch, electrons can flow from one to the other. Is that a metallic bond?

Question

If two very hot wires touch, they melt together to form one wire and electrons can flow between them.

If two cold wires touch, they do not melt together to form one wire but electrons can still flow between them (reference).

Does a metallic bond form between the two cold wires?

Is there a conceptual difference at the atomic shell/bonding level between electrons moving through a solid and electrons moving across two separate pieces of metal that are touching?

I thought metallic bonding by its very nature meant that it only existed in a single solid piece of metal. But if that's the case, how do electrons move between two separate pieces of metal if there is no bond between them?

I probably have some underlying assumptions wrong about all this, so feel free to point out anywhere my logic is flawed.

Answer 1

This becomes clear with the band theory of solids:

It is a collective quantum mechanical model for the solid state

In this model it is the collective lattice of the solid to which all electrons are bound. In the conduction band of metals the electrons can move over the whole system because very little energy is needed for a bound to the atoms electron to belong to the whole lattice, just the ambient heat is enough. So for two touching cold metals the conduction band becomes easily one topology if there is no air between the surfaces.

So it is not a metallic bond in the sense of a chemical bond, just a topological one .

In hot wires melting the atoms at the valence level bond where the melt happened and the two wires become one.