I find that the phrase “strike while the iron is hot” exists in Italian form as well, and “make hay while the sun shines” also exists in German.
The "strike" idiom is ambiguous, though. Are we to strike the iron while it is hot, or are we to strike something else with a hot iron. There are a lot of sites out there that aver the blacksmith has to flatten and shape hot iron to make a horseshoe.
That makes me suspicious, right there. If you're dealing with horseshoes, that's the work of a farrier, not a blacksmith. Undoubtedly, many blacksmiths were farriers as well, especially when we're talking of nags, but the blacksmith made more money making tools, hinges, hammer-welding, etc., and that didn't involve the danger of getting kicked by a horses. Too, the owners of race horses and other valuable horses wanted the skills of a farrier specialist, who often made “orthopedic” horseshoes to correct a stride, etc. A poorly-shod horse could easily harm himself!
A blacksmith doing hammer welding was something to behold. My great-grandfather would repeatedly move the pieces from the forge to anvil and back as he pounded the metals together, and he didn't just “pound when the iron was hot” but at exactly the right hot. If the metal was too hot, it'd spoil the work to hammer it. Hammer welding fixed a break so it was, as Hemingway would have put it, stronger at the mended place than it originally was. Arc welding, acetylene welding, etc, melts the metal, resulting in a weaker weld, but hammerwelding preserves the molecular structure of black iron.
They weren't talking of a clothes iron. Not only do you not ordinarily strike clothing, but those were called flatirons as recently as the 1930s. Branding irons are more properly pressed into the skin, rather than striking it. Andirons and tire irons are pry tools, and not normally heated. A blacksmith could make you an iron with your name or logo on it, that you could brand wood items (such as wooden shipping crates) that you would heat and strike with, but were they common in the 1300s? Striking an enemy with a hot iron would disfigure, not just inflict bruises and broken bones, but you cannot carry a fire around to use it as an offensive weapon, and as a defensive weapon, you can't wait for the iron to get hot.
In the 1700s, it appears fairly common that the phrase was “too many irons in the fire and some will burn” (or all will burn). If black iron is left too long in a forge, it almost melts. The earliest instances, though, appear to have popped up in the 1300s, and the idiom could have morphed by then.
They told a story around grandpa's shop about a neighborhood loafer who came in one cold day, saw a piece of metal in the middle of the dirt floor, and picked it up. It was hot, and was lying there to cool slowly. He didn't hold it very long, of course. Another loafer there said, “Doesn't take you long to look at one of those,” and the fellow with the burnt fingers said, “Well, youi know – seen one, seen 'em all.”
Grandpa died in 1953, in his nineties, having outlived three wives, still running his smithy, and regularly fending off women in their teens and twenties who were interested in cleaning his house, cooking for him, and keeping his bed warm, with or without benefit of matrimony. I guess hard work keeps you healthy – either that, if you're not uncommonly healthy, you can't be doing hard work for that many decades.
In any case, I don't find any explanation I can find or can fabricate, to be very satisfactory. Surely in the 1300s, virtually all would know that in a smithy, you strike when the iron is not too hot, yet that seems to be the least unsatisfactory. Perhaps it came from the speech of a preacher, politician, or other ignorant fool.
deaconB said: A blacksmith doing hammer welding was something to behold. My great-grandfather would repeatedly move the pieces from the forge to anvil and back as he pounded the metals together, and he didn’t just “pound when the iron was hot” but at exactly the right hot. If the metal was too hot, it’d spoil the work to hammer it. Hammer welding fixed a break so it was, as Hemingway would have put it, stronger at the mended place than it originally was. Arc welding, acetylene welding, etc, melts the metal, resulting in a weaker weld, but hammerwelding preserves the molecular structure of black iron.
That appears to be the correct etymology. See here and here.
Don't know about "black iron" aot to other types or alloys. Damn it Jim ... I'm a doctor, not a metallurgist. 
And finally, just because I can, enjoy this nice image of a smithy "striking while the iron is hot" ...
Heimhenge said
That appears to be the correct etymology. See here and here
I don't know much about Richard Edwards. I know about Wikipedia and Wiktionary, and consider it to be as reliable as any other anonymous graffiti.
The problem is that while popular usage determines what a work currently means (against the illiterate use of literally, the gods themselves contend in vain) the origin of a phrase is not subject to a popular mandate. It doesn't appear that Edwards was the originator of that phrase, although he well may be, nor does Edwards really state that he's talking about metallurgy.
What does "plied the Haruest" mean, anyhow? Google guesses that "Harvest" is meant, in which case, an agricultural iron may be striking something, instead of a smith beating a hunk of metal yo form it. They used a "break" (or perhaps a "break") to deal with a harvest of flax. Was Edwards talking of striking lambs with a hot iron to mark their ownership.
Please don't take this as criticism of you. If you assert something, knee-jerk reaction is to believe you, because you've established a reputation for good research and clear-headed thinking. I agree, that appears to be the correct etymology, and there's no reason to suppose that the term was lifted from a blacksmith who was pedantic about word use, but appearances can be deceiving, and I wonder if anyone has really researched this properly. As we know, there is what can be verified in scholastic journals, and then there is the actual truth.
Sorta like the etymology, for an internet flame. Dictionaries talk about it deriving from homosexual slang and drop it there. But in the 1980s, one who frequently posted abusive messages was often asked if he wore asbestos underwear, because there was obviously a flaming asshole in his breeches. Accusing someone of being hmosexual was an accentuator, but it was the "asshole" that was core too the insult; not only are you an arrogant jerk, a (ni)twit, but you were an extremely annoying one. A flaming asshole was one where hemorrhoids were inflamed by ill-use of the rectum. I was there and saw the development of that slang, but it mostly happened ion FIDO rather than on USENET and while Google bought DejaVu and saved the USENET archives, nobody did the same for FIDO. FIDO didn't have a bangpath, best I recall, and if USENET distribution was spotty before DejaVu, FIDO made USENET seem positively rigorous.
Thanks, Heimhenge. I appreciate your efforts.
No prob. Just sharing what I found. The etymology made sense to me.
Curiously, when I ran an Ngrams on that phrase (well, at least 5 of the 6 words) I found this. And the huge initial spike correlates with the rise of the Industrial Revolution. Lotsa iron got struck during that period.
But when I started searching individual citations, all I found was the phrase being used as a metaphor. Nowhere did I see instructions to iron workers based on the sound science behind that admonition. Still, I think that's surely where it came from. BTW ... searching those citations is a bitch, as most of the older stuff is scanned but not OCRed.
Heimhenge said
Curiously, when I ran an Ngrams on that phrase (well, at least 5 of the 6 words) I found this. And the huge initial spike correlates with the rise of the Industrial Revolution. Lotsa iron got struck during that period.
If you extend the time period back a century, there is a peak of 23447 in 1768, which drops to 11079 in 1803. I thought that Napoleon sold the Louisiana Purchase in 1803 to pay for a war. Lots of weapons being forged. And although I understand the secret of Napoleon's military success was the use of triage in the care of injured soldiers, there would have been many taking advantage of circumstances. I think n-grams have a lot in common with fashion, and while hemlines rise with stock prices, I'm not sure how much word fashions have to do with industrial revolution.
Are there many forged parts in a Jacquard loom? I've never had more than a passing glance in movies that were not at all about the looms. I tend to think of wooden tools in the industrial revolution. Tools weren't individually powered; they ran of a central dynamo via belts.