If only there was some way of heating up an area between the two
pieces, so both would become molten, then solidifying into a single
unit. But is that possible due to the melting temperature? It think it
melts at 2 bazillion degrees, or something like that...

Perhaps someone could construct some kind of tool that could use an
electric arc as a heat source and inert gas as a shield... I guess you
could use tungsten as an electrode and argon as an inert gas source.
You could call it tungsten inert gas welding, or "TIG" for short.....