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16. Opening the oven on Shabbos when there are still burning coals inside of it?
In a case that one knows there are fiery coals in the oven, then it is forbidden to open it through a Jew, being that [this will cause] the wind to enter it and light up the coals. Now, even though one has no intention to light them up, nevertheless [it is forbidden to open the oven] as [by opening the oven] it is inevitable [for the coals not to light up in the wind]. Nevertheless, it is permitted to do so through a gentile, being that any prohibition which occurs inevitably [when a permitted action is done], does not carry with it a prohibition to tell a gentile to do so for him, as was explained in 253 [Halacha 10].
Closing the oven on Shabbos when there are still coals burning in it: Similarly, if one wants to return and close the oven with a sheet of wood, then if it has fiery coals inside it, it is forbidden to close it through a Jew, as the wind blows through a small crack [that is in the area that has been closed]. This is similar to blowing [on the coals] as it lights up the coals even more so then if the oven had been left open. However, through a gentile this is permitted [to be done]. It is even permitted for a Jew to close it as long as he does not close it completely, and as long as he leaves much of it open. However, if he [only] leaves it a little bit open, then certainly the wind will blow inside it and is forbidden to be done.
On Shabbos may one open an oven which works on thermostat?
This is only permitted when the oven is currently on, or one left the door partially open from before Shabbos in a way that cold air can enter it, and thus by further opening the oven he is not causing a new action. However, if the flame is not currently on and the door of the oven is closed it is forbidden to open it.
Closing the oven door if the food is not fully cooked: Is forbidden.
 Admur 259:7
 Lit. “Can one cut off its head and it will not die”
 Shabbos Kehalacha Vol. 1 p. 239
 The source of this ruling [Minchas Yitzchak] is discussing a case that due to this the oven is always left on, and not when the oven is now off.
 Rav Wosner in Siach Torah 2:18; Beir Moshe 4:32; Mishneh Halachos 5:46; SSH”K 1:17; Piskeiy Teshuvos 253:8
The reason: This is forbidden as doing so will enter cold air inside and cause the flame to turn on sooner than expected due to the drop in the temperature of the oven.
Other opinions: The Igros Moshe [4:74] rules on this leniently on the basis that it is not definite that the opening of the oven will cause the flame to turn on.
 Admur 259:7