Answer-Thevelocityofheatradiationin vacuum is –

Electrons are generally responsible for heat conduction. The phonons vibrations of the nuclei also play a part, dependingonthetemperature of the medium. It depends on the specific conductor youre using. At some point, in a vacuum, the electrons have to be excited enough to spit out photons, which are Electromagnetic radiation, which in a vacuum should go on forever at the speed of light theoretically.