The cone becomes very hot stream of molten copper. It melts through the steel plate, much like a jet of hot water melts through a block of ice.
This happens fast enough that much heat does not have the time to escape from the impact site, despite high thermal conductivity of metals. The high pressure created by the explosion keeps the jet compressed from sides, too, so it does not fragment easily.
Various kinds of "active armor" trigger the munition by a thinner layer of metal well ahead of the real thick armor plate, then produce counter-explosions to break the jet.