I tried to look through the Beit Yoseph on my own, so I apologize for the gaps in (noted by question marks) and any misunderstandings I had of the text -- all comments greatly appreciated)
Beit Yoseph: Kira She-hi G'rufa v'chu -- Beit Yoseph quotes the mishna, then adds at the end that according to the gemara, Rav Sheishet says [what's "L'divrei Ha'Omer??] mahzirin (returning) means you can even return it on Shabbat.
Mem"shin: Rabeinu kol z'man she'hi rotahat -- if you leave it in your hand until the tavshil gets cold, it's assur to return it because [daled-hay-lamed ?] it's then like bishul (cooking). Rabeinu [who is this?] says in the name of the Ri -- everything that is a majority sauce and if you cook it it'll get better (mitztamek v'yafeh lo) and it's cold and it was returned to the top of the kira (and it cooks more and finishes the cooking?) and it was written in the gemara that if it didn't cool down even if there was a change in the sauciness a little you can return it and further it was written in the name of the Ri that if the food came to the point of ben drusai then it's ok to retun it but if it hasn't reached the level of ben drusai you can't return it if you left it (?)
According to the Ramban and the Rashba anything that is cooked (?) while it's still light -- so what does it matter if it's cooked when it's still day or when it's dark? If it was cooked right away after dark so then if it didn't get to the state of ben drusai while it's still day and it's still cooking and didn't get to the state (ben drusai) our Rabbis wrote in siman shin"het that if it isn't all the way cooked even if it's to the level of ben drusai it needs to get cooked even if it's still hot and after that how can we permit returning it here? If it's totally cooked, but specifically if it's not cooked all the way even if it's at the state of ben drusai it's assur to return it if there's any heat in the kira and the pot is hot from this heat.
Check out another blog:
Israel and it's Place in the World
(to the members of the HP/Edison Pirchei Shoshanim Habura/Hevra -- Please add comments, corrections, other sources. I want this to be a place where we all can share our ideas and other sources for and from our learning.)