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BOILING DOWN THE PIGS.
An iron puddler is a "pig boiler." The pig boiling must be done at a certain temperature (the pig is iron) just as a farmer butchering hogs must scald the carcasses at a certain temperature.

If the farmer's water is too hot it will set the hair, that is, fix the bristles so they will never come out; if the water is not hot enough it will fail to loosen the bristles.

So the farmer has to be an expert, and when the water in his barrel is just hot enough, he souses the porker in it, holding it in the hot bath the right length of time, then pulling it out and scraping off the hair.

Farmers learned this art by experience long before the days of book farming.
And so the metal "pig boiler" ages ago learned by experience how to make the proper "heat" to boil the impurities out of pig-iron, or forge iron, and change it into that finer product, wrought iron.