The heating of bullets in flight is hard to study. I must defer to ballisticians with more experience and equipment. But those who've conducted the Doppler trials for Hornady are on to something. As I've mentioned in my articles on the topic, heat build-up becomes consequential when the bullet 1) is going fast enough to generate requisite friction, 2) has a high enough BC to travel at speed for some distance and 3) flies far enough to permit thorough heating. Most bullets/shots don't meet all those requirements. Your question about HP and SP noses is a good one. Without data, I'll hazard that jacket material won't melt at the velocities shown to induce melting in polymer. And while lead will liquefy at lower temps than gilding metal, it's already imperfect in form at the bullet tip. If heat affects its shape, any change would be hard to measure and to replicate in shooting trials. That's my tractor-seat opinion.