In one of my previous comment I already mentioned "an average temperature of just 100 °C above the boiling point is able to produce more than 100 times its [cathode] volume in vapor bubbles.". Anyway, this is a conservative assumption. Someone reported that, in a F&P cell, cathode can reach 300°C.
Suppose it did reach 300 deg C. Heck, suppose it is incandescent red at 1500 deg C. Put it in water and in a few seconds the boiling stops. That is a fact. That has been know for thousands of years. If you do not believe me, try it yourself. The fact that it produces 100 times the cathode volume in steam is utterly irrelevant. The steam leaves the cell immediately. There is a hole in top of the cell!
This is disappointing. I wonder why such a significant document is kept secret.
It was not secret at all. It was broadcast on a major TV channel as I recall. It is lost.
You wrote that "The reaction continued far longer than any chemical reaction could have, according to the people who made the video." Does it means that you know who they are?
It was made by F&P and a TV reporter. I don't recall who.
"normal" nail is what everyone has usually at home for hanging a frame on a wall. And its diameter is much less than the 4 mm of the F&P cathode.
This is ridiculous. You can buy a box of large nails, or you can heat up a dozen small nails, or use any piece of steel approximately this size. Stop with the bullshit and evasions. Try it, or shut up. Make a video showing an incandescent nail boiling water for 20 minutes with no input power. You will win the Nobel Prize.
At second 35, the image change almost immediately after the blacksmith immerse the piece of steel into the barrel of water. The same happens for the next image, when the piece of steel is put in a transparent vessel. How can you say that "within a few seconds boiling stops"?
Watch the video and you will see that in few seconds, the boiling in the transparent vessel has nearly stopped. Or look for another video. Or TRY IT YOURSELF, for crying out loud.
Anyway, your making reference to that video means that you have not well understood the difference between a barrel of cold water and a well insulated Dewar bottle containing well stirred water at boiling temperature. In the first case you have a huge sensible heat capacity for quenching the pieces of metal, that is the cool water has plenty of room to increase its temperature before reaching the boiling temperature. On the contrary, the boiling water in a F&P cell has no more sensible heat capacity, it can't no more absorb heat by increasing its temperature.
This is complete and utter bullshit. The steam leaves the cell immediately. It goes right out the top, because the cell is open. If the water temperature is already close to boiling, the temperature does not increase. The water vaporizes and leaves the cell, carrying off the enthalpy. Try it with a Dewar if you do not believe me. (Never mind. You will never try anything, or believe anything, even common knowledge going back 7,000 years, to the beginning of the iron age.)