In 1532, Henry VIII of England decreed that anyone convicted of poisoning another person would be put to death by being boiled alive in a cauldron of hot liquid. This form of capital punishment had been all the rage during the Middle Ages, so he had plenty of precedent.
But he didn't specify whether the boilee should be immersed in oil or water, two common liquids that were available in quantities large enough to surround even a poisoner his own size -- estimated from measurements of his armor to have been 6'3" tall with a 52" waist and weighing about 300 pounds. Both liquids were undoubtedly used, but the phrase "boiled in oil" has become favored by writers and historians because of the echoing diphthong sound "oi."
Now I hate to spoil a king's fun, but as all cooks know, oils won't actually boil; they just get hotter and hotter until they begin to smoke. And just how hot does a cooking oil have to get --its so-called smoke point -- before smoking? In spite of what you've read or heard, there is no definite answer to that question. Hot oil begins to smoke gradually over a range of temperatures, and even that range can't be depended on. Anyway, what do you call "begins to smoke"? A wisp or a cloud?
When heated, most liquids eventually reach a temperature at which they boil -- that is, turn into vapor. That standard boiling point of water, of course, is 212 degrees F. But long before a vegetable oil can even think of boiling, it suffers a molecular breakdown; it decomposes into acrid fumes and smoke. The breakdown begins slowly, not at any precise temperature, like a boiling point.
More problematically, there is no such thing as a typical bottle of safflower or peanut oil, or any other kind, for that matter. The smoke point of a given sample will depend on how and where the seeds were grown, how the oil was extracted, and especially how it was refined. So those official-looking charts of smoke-points you'll find in food references are only the roughest guide to when the oils will set off your smoke alarm. Don't take them seriously. The wide variations from chart to chart are a tip-off to the fact that they're little more than shots in the dark.
While writing my book, What Einstein Told His Cook; Kitchen Science Explained, I tried to find a consistent and authoritative set of temperatures to quote, but I had to give up. Instead, I included only a bar chart of the approximate ranges for the various oils.
Note that all the smoke points you may find quoted are for fresh oils. When oils are heated or exposed to air, they release free fatty acids, which both lower the smoke point and taste rancid. In particular, high-temperature deep frying oil will break down and smoke quite readily. Moreover, hot oils tend to polymerize -- their molecules join together to form frequently toxic, big molecules that give the oil a thick, gummy consistency and a darker color.
The easiest indicator of breakdown, then, is not so much smoke as discoloration. All things considered, discarding deep frying oil after one or at most two uses is safest and best for both health and palate.
You still want numbers? Okay, here are the approximate ranges of smoke points for some common fresh oils in degrees F, according to the Institute of Shortening and Edible Oils:
Safflower 325-350
Corn 400-415
Peanut 420-430
Cottonseed 425-440
Canola 435-445
Sunflower 440-450
Soybean 440-450
Olive oil is a special case, because there are so many kinds that generalizations are hard to make. Its smoke point can be anywhere from 280 to 400 degrees.
Notice that most of the temperatures are clustered between 400 and 450 degrees, so there's no need to get all edgy about which one will smoke least. Just use be prudent about turning up the heat. And remember that a little smoke won't kill you. That's what range hoods are for.