hot and cold working
Metals are shaped by squeezing and stretching them plastically: rolling, forging, extruding, drawing. Whether that shaping counts as hot or cold work is not about how warm the metal feels but about one temperature, the recrystallization temperature. Work the metal above it and it is hot working; below it, cold working. That single line divides two very different behaviors.
In hot working the metal recrystallizes as fast as you deform it, so new soft grains keep replacing the strained ones and the metal never hardens; you can push it into huge shape changes (a steel ingot to a beam in one heat) with modest force, and it ends up soft. In cold working the metal cannot heal, so dislocations pile up and it work-hardens: force rises and ductility falls as you go, limiting how much you can do before it cracks, but the part ends up stronger, with a clean surface and precise dimensions. The same recrystallization temperature that defines the boundary is set relative to melting point, so it is metal-specific.
Each has its place. Hot working (hot rolling, forging, extrusion) does the heavy early shaping cheaply and breaks up cast structure, but the hot metal oxidizes to a rough scaled surface and its dimensions are loose because it shrinks on cooling. Cold working (cold rolling, wire drawing, stamping) finishes the job to tight tolerance and bright finish and adds strength, but needs more force and periodic annealing to restore ductility. A typical product is hot-rolled to rough size, then cold-rolled and annealed to final strength and finish; the two are partners, not rivals.
A steel beam is hot-rolled near 1100 degrees C, where it stays soft no matter how much it is shaped; the same steel made into a drink can is cold-rolled at room temperature to gain strength and a smooth surface, then annealed between stages so it does not crack.
Above the recrystallization temperature the metal re-softens as it deforms; below it, deformation hardens it.
Hot and cold are relative to the recrystallization temperature, not to human comfort; deforming tungsten at 1000 degrees C is still cold work, while deforming lead in your hand is hot work, because lead recrystallizes below room temperature.