yitay: nice chabura. I thought something a little simpler.
1) It seems Pashut to me that it is impossible to have either Bishul or Bliyos in something that remains very cold. Therefore, while I have numerous proofs that the Sugya must be discussing where both ended up hot, I think they are superfluous.
2) There are 2 possible ways of explaining ???? ???, in my opinion. Either the dispute relates to the Metzius of whether the cold one became hot or not, or it is assumed hot and the dispute is whether it has a Din Bishul similar to a Kli Rishon or no Din Bishul similar to a Kli Sheini.
That will have to wait for a different day.