I suspect how fast the cooking oil was heated up makes no difference in how fast it will cool down.
But that having been said, it is important to list some of the
things to be careful about in an experiment to test this, and under
what circumstances the above claim can be wrong. First of all, if you
heat the cooking oil up in a pan on the stove quickly, then you have to
turn the stove's burner or heating element way up high. The pan, and
whatever it's touching will get hot too, not just the oil. Even if the
final temperature of the oil is the same if you heated it up quickly or
slowly, the temperature of the parts of your stove may not be, and
these may take longer to cool down if they are hotter. You can control
the experiment better by taking the pan with the oil off the stove.
There may still be bits of problems -- if the pan doesn't get uniformly
hot (say the edges, or if you have a lid, that), it can affect the
results of an experiment. If the oil is not all at the same
temperature, that can be a problem. Oil heated up slowly, I would
guess, may have a more uniform temperature throughout, while oil that's
heated up quickly may have hot spots and cold spots. Convection is
supposed to make these differnces go away, but if you only have a thin
layer of oil in your pan, convection can be hindered. To control for
this last effect, you could stir the oil around before measuring its
temperature, just to make sure the temperature measaurement reflects
the real temperature of the oil.
One last thing -- if you heat oil for a really long time (that is,
heating it up really slowly, say, over the course of days), then some
of the components of the oil which evaporate more easily than others
will do so. Then the oil may be gummy as it cools down, and may cool at
a different rate becuase convection is hindered.
Naturally you have to control all the other variables in the
cooling-down part of the experiment very carefully -- air temperature,
the temperature of anything touching the pan, and air flow rates. Can
you think of other ways external factors can affect the experiment?
(published on 10/22/2007)