If a person forgot to put a blech on the stove, can he do it on shabbos? Sources would be appreciated.
There are different opinions (see here for example).
The Shemirat Shabbat KeHilchata 1:23 and 1:38 permits it, only if the fire is not that strong enough to make the blech "red-hot".
In footnote 33, Halachipedia says:
Sh”t Zera Emet 3:26 permits one to put a metal tray (with small holes) on a fire on Shabbat and then do Hachzara based on S”A 318:8 where he brings the dispute whether one can do Hachzara on an empty over the fire and rules like the lenient opinion. Chazon Ish 37:11 argues that actually placing the metal sheet on the fire is the forbidden act of Mavir based on Rambam (Shabbat 12:1, 9:6) who says that one who heats metal to mold it violates Mavir. Even though S”A 253:3 writes that on Shabbat day one can put a empty pot on a fire (and then return a pot that was on the fire right before), Chazon Ish explains that S”A is talking about a earthenware pot and not metal. However Nishmat Adam 20:1, Kesot HaShulchan (134 pg 42), Sh”t Shevet Halevi 1:91, Sh”t She’ilat Shaul 29, Chazon Ovadyah (Shabbat 1 pg 55), and Sh”t Tefilah LeMoshe 1:59 (pg 647) argue that in our case the tray won’t become hot as a coal or hot enough to be reshaped and so it should be permitted. Shemirat Shabbat KeHilchata 1:23 and 1:38 permits covering the fire on Shabbat as long as the fire isn’t strong enough to make the tray red-hot.
See also this article.