We've got a strange case of synchronicity here with the thread on the Brookhaven quark plasma experiment. The temperature there, confined to a nuclear radius or so, of a fireball induced by collisions of gold nuclei, is a few trillion degrees Kelvin ... enough to "melt protons" , as noted.
You wouldn't have to melt protons to get rid of radioactive nuclei, but you would have to melt the nuclei. This would require a temperature of a few MeV, vs. the 100 MeV corresponding to the trillion degrees. So we're talking a few billion degrees Kelvin. Compare this to the mere 10 million degrees Kelvin at the center of the sun.
Good point. The larger the nucleus, the hotter you have to make it in order to fuse with other nuclei. The Sun causes significant amounts of fusion among only the first few elements; Hydrogen, Helium, and maybe one or two more.
The heavier elements are produced only when stars explode, there’s a Big Bang, or we make a nuclear explosion. I have read that a nuclear fission bomb creates temperatures that create transuranics—elements heavier than Uranium—all of which are highly radioactive, so they have very short decay times. (Because of those short decay times, no transuranics are found naturally on Earth).