Lead tipped bullets can have the exposed lead melt while in flight, something I can prove by targets that show tiny "comets" or curlie-cues of lead on the paper. This takes a velocity that's pretty high, something close to 4,000 fps (possibly less, I don't remember the exact number).
As to core lead melting, I would guess that little more than a few molecules of thickness of lead would become liquid *if the jacket were significantly spinning around the core.* This is something I am not aware of although it certainly could be possible. However, considering the time of flight and the fact that the core is accelerating at the same speed as the jacket, any difference in temps between the jacket & core shouldn't be that great. Enough to cause melting? Beats me! Off hand, I would more easily accept some jacket slipping around the core while in flight, which would not involve any melting of lead at all. Lead is a fairly decent lube when under pressure but enough to allow the jacket to actually spin? Again, I have no idea! Add in that there are so many other factors, bullet diameter, launch speed, lead composition, lead/copper pressure during manufacture.... it becomes a huge, and probably expensive, problem to solve!
Cheers,
crkckr