Is it permitted to raise or lower the flame under a blech, after the food has been placed or does one need to remove the blech if they want to change the setting on the flame?
The reason why we place a blech over the stovetop is because chazal were afraid that if we have partially cooked food on the stovetop, we might come to play with the fire. Therefore, they prohibited keeping a pot of partially cooked food on the fire (called shehiya). One of the ways to avoid this issue is by placing a blech over the fire. When a blech is placed over the fire, it lowers the placing blech over the fire helps, and since the person showed that he doesn’t want a higher fire we are no longer afraid that he will make the fire higher. The poskim discuss if we may raise the size of the flame after placing the blech over the fire, because in a way it is showing that we still want a high fire. In fact, a number of poskim say that it is preferable not to raise the flame after the blech has been placed on the fire. It should however be noted that such a scenario is not that common. This is because if the food on the blech has already been cooked, or even if it is already half cooked, and the only reason the blech is needed is in order to do chazara, the fire may be made higher. This is because the main reason for the blech then is so it shouldn’t look like cooking, therefore raising the fire is not going to matter here. Therefore, since most of our pots are indeed at least halfway cooked before Shabbos comes in, this issue is largely theoretical.
Shmiras Shabbos Khilchoso1 ftnt. 63,217, Shvus Yitzchok 2 pg. 22, Halacha Shleima 2 9 D:H v’chain.