kli rishon and sheni

Question

Regarding utensils used to cut meat… Does food that is still very hot placed on a kli sheni have the statutes of a kli rishon? If yes what temperature is the cut off, 125 degrees? Also, when the food inside the keli rishon (off the heart source) cools down, does it loose the status of a kli rishon? If yes, what temperature is the cut off, 125? I am trying to discern if the kashrus implications of kli rishon and sheni are temperature based or halakhic doctrine. Thanks