Is it ok to take food already cooked of an already heated coil burner and after its cooled put it back on an already heated coil burner?
Thank you for your question.
There is an idea that fully cooked food that is dry, (without sauce or liquid) may be placed on a heat source to reheat on Shabbos. However, placing it on a coil burner would not be allowed. The reason is because placing the food on the coil burner or any other exposed heat source, appears to be cooking. What you can do is to place a metal cover over the fire, (called a blech) before Shabbos, then on Shabbos, take a pan, an aluminum pan, or even a plate, place it upside down on top of the blech, and then you can put your dry cooked food on top of that to heat up.
O:CH 253-5, Shmiras Shabbos Khilchoso 1-44 ftnt. 126.