We know that a food that is a "davar yavesh" (dry) that was already cooked (in a cli rishon) before Shabbos may be put into a pot of hot water (even a cli rishon -- so long that it is on the fire) on Shabbos (See Orach Chaim Siman 318 Saif 4.)
We also know that in general a food that wasn't cooked may not be put even into a cli sheini (that is yad soledes bo) on Shabbos. The reason for this is either because we are afraid of "kalei habishul" foods that are easily cooked (even in a cli sheini) and since we don't know what foods are and what foods aren't we are therefore machmir by all foods. Or because of the reason that if the food wasn't cooked and now it's going into a cli sheini it could be considered "mechzei c'maveshel" (it "looks" like we are cooking.)
With this in mind, what would be the din if someone put a food in a cli sheini (that's yad soledes bo) before Shabbos. May it be put now into a cli sheini on shabbos?
If the food is considered to be from those that are "kalei habishul" then you could say that it's muter because it's already been cooked and would have the same din of a regular food that was put into a cli sheini. There is then no problem of actual bishul or even "mechzeh c'maveshel." However if the food is not considered to be from those that are "kalei habishul" (let's say we know for sure) and it was already in a cli sheini that was yad soledes so "something" happened to it. Would that be enough to take away the second problem of mechzeh c'maveshel when one puts it into a cli sheini that is yad soledes bo on Shabbos?