Heating plasma to higher and higher temperatures does not cause ions to decompose into individual protons and neutrons. In fact, at extremely high temperatures, the particles in the plasma become highly energized and dissociate into a state called an "ideal gas." In an ideal gas, the charged particles (ions) are separated from their electrons, resulting in a mixture of free electrons and positive ions.
As for the decomposition of protons and neutrons into quarks, this process occurs at much higher energy scales than those typically reached in high-temperature plasmas. Protons and neutrons are composite particles made up of three quarks each. The quarks are held together by the strong nuclear force, which is stronger than the electromagnetic force. Breaking up protons and neutrons into their constituent quarks requires extremely high energies, typically found in high-energy particle colliders or in the early universe during the first moments after the Big Bang.
When matter is subjected to extremely high temperatures and densities, such as those present in the early universe or in certain astrophysical objects like neutron stars, a state of matter known as quark-gluon plasma (QGP) can be formed. In the QGP state, the quarks and gluons are no longer confined within individual protons and neutrons but instead exist as a deconfined state. This phase is considered a new state of matter, distinct from the familiar solid, liquid, gas, and plasma states.
To summarize, heating plasma to higher temperatures results in the dissociation of ions into free electrons and positive ions. Decomposing protons and neutrons into their constituent quarks requires much higher energies, typically found in extreme conditions such as high-energy colliders or the early universe. The resulting state of deconfined quarks and gluons is known as quark-gluon plasma, representing a novel state of matter.