Soup in a keli sheni

Dear Rabbi, Is there a concern that if one adds a hot liquid (for example soup) to a keli sheni (I understand that if one has used a ladle, the ladle can be a a keli sheni and the next vessel is a keli shlishi, but for argument sake one did not use a ladle and now has poured soup directly into another vessel) that already has some soup liquid in, but is now cold,is there is a concern of the already cold soup being heated/cooked?

לז"נ אברהם יוסף בן אלטר משה ז"ל ב"ה Shalom The ladle is considered Kli Sheni only if it has not stayed in the pot. If the ladle stayed in the pot it attains the status of a Kli Rishon(See Shmirat Shabbat Kehilchata- Hebrew edition, Vol. I pg. 33. Chap. 1: 54 &68 and notes ad loc.) You may pour the soup directly into your Kli Sheni plate with soup only if the soup is still warm. If the soup is already cool you may not pour hot soup on it directly from the pot. This is the Ashkenazi practice, while Sephardim are more stringent and if the soup in the bowl is not actually hot, you may NOT pour hot soup on it from the pot. (See Shmirat Shabbat Kehilchata, Hebrew edition, Vol. I pg. 26, Chap. 1:53 , Shlchan Aruch 318: 4 & 15) If you wish to see more details in English, you can see online, or download the app. for free, of the the book Pninei Halacha, by Rav Eliezer Melamed Shlit"a , ( the son of Rav Zalman Melalmed Shlit"a ,the founder of this site) on Hilchot Shabbat. All the best May we see the building of the Bet Hamikdash in our time.