Protons are Usually in Nuclei
Protons are usually located in the nuclei of atoms. Because protons are usually in the nuclei of atoms, they are held really tightly by atoms. It is extremely difficult to remove a proton from an atom. As a result, even though protons are charged particles, they are not typically the charged particles involved in heat conduction or electric current.
However, if the entire nucleus of an atom can move (as is the case in liquids), then protons can move and can contribute to heat conduction and electric current.
However, if the entire nucleus of an atom can move (as is the case in liquids), then protons can move and can contribute to heat conduction and electric current.