This is nothing but trickery. In this particular case, it appears that they have a liquid in there that has a much lower boiling point, is heavier than the oil, has the same appearance as the oil, and it is boiling to give the appearance that the oil is boiling. In this particular case, lemon juice is the common liquid used.
Experiment – 22
Effect: The hand is dipped in boiling oil without getting burnt
Props: One frying pan to hold about two liters of oil, one liter cooking oil, stove and one lemon (big).
Method: Pour the cooking oil in the pot with the lemon juice squeezed in the oil stealthily. Place it on the fire. Before the oil get hot and boiling, the lime juice settled at the bottom of the pot boils first and oil appears to bubble when the steam is released. It seems as if the oil is boiling hot. Immerse your hand in the oil and take it out. The boil will be only warm and not boiling, though it looks like boiling oil to the viewers.
This is a relatively well known phenomenon amongst people who practice scientific skepticism and debunk charlatans. The dismaying thing is the credulity with which the press reports these stories...
The other "trick" is also detailed on the experiment. Basically, you put one thing in, and it absorbs heat as you get the other thing out. In this case, it's "poories" instead of chicken, fries, or fish, but the principle is the same.
Experiment – 23
Effect: Frying poories in boiling oil and taking them out by hand.
Hot bajjis are being taken out of boiling oil with bare fingers
Props: Wheat flour or maida flour, water, plate, instrument to make poories, cooking oil and a stove.
Method: Prepare poories with the flour (one dozen). Boiling the oil, put in the oil, poories and as soon as it is fried, put underneath the fried poorie an unbaked one and pick up the fire one by fingers, it will not burn. Beforehand apply the same oil on your hand.
The science behind this feat is that when you put a fresh poorie under the fired one, the heat of the top oil is absorbed by the fresh one, and your fingers will not et burn. The oil applied on the hand before dipping also insulates the hand.
I should add, as the web page I pulled this from also states it:
(Note: Those items involving fire and other dangerous substances should be performed only under proper guidance)
In other words, don't do this yourself kiddies! It's still dangerous, especially if you mess it up. Remember, this is an area of the world that loves their supernatural explanations as opposed to rational explanations. Sanal Edamaruku faced up to three years of imprisonment for showing a "weeping" statue was actually due to a backed up sewer line...