Q) Is it mutor on Shabbos to return a pot of (cooked) food to an oven that is warm but not hot (i.e. less than yad soledes bo)?
A) The Magen Avraham (OC Siman 253 s.k. 9) discusses this very point and says that if the oven is not yad soledes bo it is permitted to place food on top of it on Shabbos, and it may also be allowed even if the oven is not goruf v’kotum. However, the Magen Avraham concludes, it can be inferred from [Siman 253] Se’if 5 that it is forbidden to place food inside a [warm] oven on Shabbos.
The Magen Avraham has no clear conclusion – as to whether or not it is permitted to place food inside a warm (i.e. less than yad soledes bo) oven on Shabbos.
The Remo that the Magen Avraham is referring to (Siman 253 Se’if 5) quotes two opinions as to whether one may place food inside a warm oven on Shabbos. The Remo then adds that if the temperature of the oven is yad soledes bo – it is forbidden.
It appears from the context of the Remo in his second comment that the two opinions regarding whether or not one can place food inside an oven on Shabbos are discussing an oven that is less than yad soledes bo. Presumably, this is the source of the Magen Avraham that there may be room for stringency even in an oven that is less than yad soledes bo.
However, it is difficult to accept that the Remo in Se’if 5 is discussing an oven that is less than yad soledes bo because the Remo himself in Se’if 2 writes clearly that if an oven is less than yad soledes bo it is permitted to return food inside it on Shabbos – and he makes no mention of any differing opinion.
The Vilna Gaon (Bi’ur Hagro 63) makes a small but significant amendment to the Remo in Se’if 5: instead of “v’im hachom… yad soledes bo” the line should say “she’im hachom… yad soledes bo”. The implications of this amendment are very significant; that there is no opinion in the Remo that is stringent with regards to an oven that is less than yad soledes bo – since the two opinions in the Remo are only discussing yad soledes bo.
The Mishna Berura (s.k. 92, 93) follows the amendment and view of the Vilna Gaon and rules that there is no room for stringency if the oven is less than yad soledes bo (see also Sha’ar Hatziyun s.k. 93).
In conclusion: although the Magen Avraham does raise the possibility that one may not return food on Shabbos to an oven that is less than yad soledes bo, however from the Remo himself in Se’if 2 and from the amendment of the Vilna Gaon and the ruling of the Mishna Berura we see that it is permitted to place food inside an oven on Shabbos if the oven is not yad soledes bo.