"Cold iron" is not about physical temperature, nor about forging.
It is about the things the fae are sensitive - emotional/spiritual/magical content, or the lack thereof, and symbolism. Iron is cold in the way that a person who lacks empathy is cold. It represents mankind's separation from the natural world, or humans taking command of their own fate in defiance of the magics of the past. Iron, and the technologies that come with it, are what allows people to no longer be subject to the whims of the world, and the whims of the fae.
Humans are natural, so anything they make is also natural.