Each player shuffles the cards from their hand into their library, then draws that many cards.
Metalcraft — If you control three or more artifacts, Molten Psyche deals damage to each opponent equal to the number of cards that player has drawn this turn.
If a player doesn’t have any cards in their hand, the player will still shuffle their library.
The metalcraft effect counts all cards each opponent drew for any reason during that turn, not just the cards those opponents drew due to Molten Psyche’s first effect.