Answer: The Shulchan Aruch (OC 253:2) writes that one may return a hot pot of cooked food to a flame providing that the flame is covered. The Rema adds that one should not put the pot down elsewhere before returning it to another heat source (chazara), and they must have intended to return it when removing it. The Biur Halacha discusses whether one needs all of these conditions in order to replace food (See Shemiras Shabbos Kehilchasa 1:18).
R’ Moshe Feinstein (Igros Moshe OC 4:74 Bishul 38) writes that one may move hot food from one blech to another even if the fire went out, just as one may move food from one flame to another, providing that one didn’t plan on the flame going out. If one purposely set one’s timer to go off at a certain time, however, they have demonstrated that they did not intend to return it to the flame.
Likewise, R’ Shlomo Zalman Auerbach (quoted in Shemiras Shabbos Kehilchasa 1:n69) held that there is a difference between actively removing a pot before placing it elsewhere, whereby one demonstrates that one isn’t planning on returning it to the flame, and a flame accidentally going out.
Nonetheless, R’ Yehoshua Neuwirth (Shemiras Shabbos Kehilchasa 1:23) writes that one should ideally not place the food directly onto another blech, but only onto another pot or upturned plate, etc.
There is a machlokes among sefardi poskim, however, as to whether they can transfer food in this scenario (See Kaf Hachaim OC 253:46; Yalkut Yosef, OC 253:10).
In conclusion, one would be allowed to transfer food providing it was fully cooked and still warm from a hotplate that had switched off to another on Shabbos. It is ideal to place it on top of something else rather than place it directly onto the hotplate.