@saitoh514 I haven't read the web novel, so it may be different there. But in this manga... if you swap the boxes for heating/cooling with quenching, then you have a very simplistic view of the process. He doesn't get into annealing at all, and god knows where a blacksmith in the forest is getting high carbon steel, but you at least get the concept of shaping, austenitizing with the quench, and tempering with the heat/cool cycle. If you swap the boxes.
Perhaps a translation error?