Why does hot oil inflame when windows are opened? A Japanese Youtuber posted a video on her survival from burns on one side of her face. She said left oil heating on the stove and noticed it producing lots of black smoke- hit the smoke temperature point of the oil.  She turned off the stove and opened windows. Then it burst into flames. Was it just that the smoke was preventing air getting at the hot oil and the in gust of air swept the smoke again and allowed the oil to get sufficient oxygen to burn but surely the oil was hotter before the stove was turned off and it had an obvious flame to trigger the fire so was something else going on here. When was opening windows the trigger for the flames?
 A: Cooking oils and fats, have on average a smoke point between 350 to 450 degrees Fahrenheit.
The flash point of oil (or any flammable liquid) is the minimum temperature at which the liquid can form a combustible mixture in air. This means its vapors can be ignited by some source. This is usually the source of heat that is cooking the oil - a gas burner or electric stove.
In this example, it is important to also define what's called the autoignition point. As per this link:
"The autoignition temperature of a substance is the lowest temperature in which it spontaneously ignites in a normal atmosphere without an external source of ignition, such as a flame or spark. This temperature is required to supply the activation energy needed for combustion. The temperature at which a chemical ignites decreases as the pressure or oxygen concentration increases".
Note very well the parts I have put in bold. Especially the point about chemical ignition occurring at lower temperatures the more oxygen is provided.
Fire needs oxygen to sustain itself, and opening a window provides oxygen flow which when combined with the hot oil will result in combustion. The oil must have been heated beyond the autoignition point, and as you pointed out, one of the needed ingredients for combustion, namely oxygen, was not present (when there was a lot of smoke) even though the oil temperature may have been beyond its autoignition point.
Barring some other event, like a random or undetected spark, then this would explain why there was sudden combustion i.e., the addition of oxygen. A small amount of time$^1$ would have lapsed from when the flame was turned off to the point of ignition. This means that the temperature of the oil would not have dropped significantly (below the auto-ignition point) during this time.

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*The time it takes a substance to reach its auto-ignition temperature $T_i$ can be calculated using the auto-ignition equation, $$t_i = \frac{\pi}{4} k\rho c [\frac{T_i - T_0}{q}] ^2$$ where $k$ is the substance's thermal conductivity, $\rho$ is its density, $c$ is its specific heat capacity and $T_0$ is its initial temperature.

