Poopular Science eh.
I have never heard of proposals to destroy any atomic nucleus thermally. If underground magma got hot enough to generate the plasma energies required to literally collide nuclei, life wouldn’t be able to exist on the planet. Unless you’re Al Gore in which case you can fake the millyuns of degrees involved.
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.