Since it a Kli Sheini it will not cook anything even if it is a high temperature higher than Yad Soledet, it will not cook.
Explanation:
The Gemara Shabbat 40b: Kli Sheini does not cook…
There is a big discussion as to why a Kli Sheini doesn’t cook.
Tosfot (Dh V’Shema) explains: A Kli Rishon sits on the fire so the walls of the pot become extremely hot and they keep their heat for a very long time. Therefore, they said that as long as it is Yad Soledet it cooks and it is forbidden to put uncooked food in it. Kli Sheini even Yad Soledet is permitted since it’s walls aren’t hot, it slowly gets colder.
Tosfot understands that the reason a Ki Sheini doesn’t cook is that to cook something the Kli has to continue with the same heat or more but since the walls are cold, the temperature drops, so even if it is Yad Soledet now, it can’t cook anything.
The Yerushalmi (Shabbat Perek 3 Halacha 4) seems to argue on Tosfot’s reasoning: What is the difference between Kli Rishon to Kli Sheini.? R’ Yossi said here it is Yad Sholetet and here it is not. R’ Yonah said neither of them is Yad sholetet just they made a decree by Kli Rishon but not by Kli Sheini.
In Halacha 5: What is a Tavshil (cooked food) anything which the fire is underneath it.
The Pri Megadim writes that Tosfot didn’t quote the Yerushalmi because they felt The Yerushalmi argues with the Bavli. The Yerushalmi understands that food can’t cook unless there is flame underneath it therefore, they made a prohibition on Kli Rishon sine it was on the fire. They did not prohibit Kli Sheini since it was never on the fire. The Bavli is of the opinion that even in a Kli Rishon not on the fire, food can cook. There was a possibility of decreeing on Kli Sheini but Tosfot says that there is a strong reason why not to because it can’t cook since the walls are cooling off.
The Gr” a (YOD 105:13) argues that there is no Machloket and when the Yerushalmi writes that in order to cook yon ed a flame, it means the that at some point there was a flame even if there is one now.
Most Poskim follow the Pri Megadim that there is a machloket and use the reason of Tosfot.
The Taz (YOD 92:30) Someone who takes water or kettle with a ladle and leaves the ladle in the kettle the water in the ladle is not considered a Kli Sheini. As Tosfot says if the wall stays hot there is the possibility of cooking so the ladle in the Kli Rison stays hot so it is a Kli Rishon.
The Chavot Daat (Biurim 27) raises a point that how can you extrapolate this from Tosfot. Tosfot is contradictory. In the beginning of Tosfot they write that it is a Kli Rishon since it has hot walls, therefore if the walls are not hot then it has to be a Kli Sheini. The end of Tosfot says that a Kli Sheini is when the walls are cooling off so if the walls are not cooling off then it is a Kli Rishon. So, the ladle fall is the middle. That is the Machloket the Rema and Maharshal.
The Rema (YOD 105:3) writes that a sold food that was placed in a Kli Sheini has the din of a Kli Sheini. The Maharshal and the Shach say solid food (Davar Gush) taken out of a Kli Rishon has a halacha of a Kli Rishon.
It is the same issue by a thermos.
The Yalkut Yosef 118:54 writes: some a Kli Sheini does not cook, that is by Davar Lach, liquid, since the walls of Kli cools off the Liquid, but a solid food like rice or a piece of meat and the bracha of Kli Rishon as long as they are Yad Soledet. Some argue that there is no difference and no such thing as a Davar Gush that Kli Sheini can’t cook, and this is the basic Din…
Halacha 55: So to it is permitted to pour hot water from a thermos into a cup with cold milk even if here is a little milk since the Thermos is a Kli Sheini it does not cook.
What about the temperature?
The Minchat Shlomo (Chelek 2:6) writes: The Rabbeinu Yonah says that definition of what cooks is that is it Yad Soledet and that I can cook other things. a Kli Sheini even though it can be very hot and can that up other liquid to Yad Soledet cine it can’t cook solid food the is no Bishul.