Is one allowed to place permissible (dry) food on top of a blech/hotplate on Yom Kippur for children to eat?
Concerning a regular electric warming plate, which can be used for keeping food warm but not for actual cooking, Rav Moshe Feinstein (Iggros Moshe, vol. 4, no. 74, sec. 35) permits placing food directly on the plate, because this is not considered an ordinary method of cooking (based on Shulchan Aruch, OC 253:5).
Many authorities do not mention this leniency (see also Shemiras Shabbos Kehinchasa 1:25), and some do not rely on the heiter. I heard from Harav Scheinberg zt”l that one may rely on it. A common custom is to place something on top of the hotplate, such as an upside down pan, and place the food on it, and this is recommended.
This ruling applies to Yom Kippur just as to each Shabbos. It applies specifically to electric hotplates and not to a blech, which can be used for cooking.
It moreover applies specifically to dry food, and not to liquids or to foods that have a significant amount of sauce.