Covered Flame-Radiator, Heater:[1]

It is forbidden to place food on top of a covered flame, in order to warm it up, unless all the six Chazara conditions are fulfilled.[2] This applies even if the area is not Yad Soledes. However, if one places another item on top of the radiator [i.e., a pot], then one may place food on top of that item for it to heat up, if the heating of the food does not contain a cooking prohibition [i.e. the food is fully cooked, and is dry or contains liquid which is still warm].

Heater/radiator-Heating food on a heater or radiator:[3]Any food which does not have a cooking prohibition [meaning it is fully cooked and dry, or contains liquid that has not fully cooled down] may be placed on top of a radiator to heat up on Shabbos.[4] However, food which has a cooking prohibition may not be placed on the heater, even before it is turned on, and if one did so then he must remove the food prior to it turning on.

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[1] 2^nd opinion and final ruling in Admur 253:26 “There are opinions which say that even if [the solid covering of the oven] is not Yad Soledes, [nevertheless] one must now place something under the pot in order to separate between the pot and the coals in the oven, in order so this serve as a reminder [of the prohibition to stoke the coals] and thus one will not come to stoke the coals. This opinion is the main Halachic opinion”; Admur 253:22 “For this reason it is proper to be careful to not remove the pot off from the Kirah or the Tanur which it was cooked in and place it [On Erev Shabbos] close to sunset, on a heater, which is not swept or covered, if it that area is Yad Soledes there. [This however is] with exception to if one places something under the pot, just like one is required to do on Shabbos itself, as will be explained [in Halacha 26].”; M”A 253:31

Other Opinions in Admur: Based on the law which permits heating a food on top of a pot, one can say that our ovens which have a [solid] covering [over the flame], even if its [coals] are not swept or covered, as wells as heaters, which [their coals] were not swept or covered, and even if the heater has fire inside it, then [nevertheless] it is permitted to place food on top of it on Shabbos even if that area is Yad Soledes, so long as this food is also allowed to be placed on top of a pot which is insulated on coals. The reason for this is because since the [solid] covering separates between the fire and the pot which contains the food [therefore it is similar to placing food on top of another pot that is on the fire]. [Admur ibid]

[2] The reason: [Although the solid covering of the oven already serves as a separation between the coals and pot, nevertheless] the solid covering [being that it was] already previously made, it does not serve as a [proper] separation or reminder to prevent one from coming to stoke the coals. [Admur ibid]

^[3]  Shabbos Kehalacha pages 409-410; Piskeiy Teshuvos 253:28; Igros Moshe 4:74-34; Bris Olam Amira Lenachri 16-8

^[4]  As this is not the usual way of cooking and thus does not appear like one is initially cooking the food on Shabbos. So rules the Igros Moshe and the Sheivet Halevy. Now although in 253:26 the Alter Rebbe seems to rule clearly that this is forbidden, and that one must place another vessel on top of the heater, Rav Farkash explains that the Alter Rebbe was only referring to a type of heater that although was not used to cook food, but was used to heat up food, while today our heaters since they are not used at all to heat up foods, therefore it is allowed to place fully cooked food even directly on them.