Is it a problem to pour hot water into a Kli Sheni that still has drops of water in it from being used previously? What about pouring from a Kli Sheni into a Kli Shlishi that still has drops of liquid from being used previously?
When making a cup of coffee or tea on Shabbos, it is common to pour boiling water into a cup that was previously used for hot water or was rinsed with cold water. This raises the question of whether this would be considered Bishul (cooking), since the boiling water affects the small amount of cold water left in the cup from prior use.
The Halachah is that, strictly speaking, Irui (pouring hot water) is a problem on Shabbos only when water is added to solids, not to liquids. However, there’s room for stringency if one is adding a comparatively large amount of hot liquid to a small amount of cold liquid. Therefore, it’s advisable to wipe the cup dry before adding hot water. However, if the water from the previous use was originally hot and then cooled off, and especially if it’s still slightly warm, then there’s no problem with pouring hot water over the remaining drops of water in the cup.
Reusing a ladle that has some solid food left on it from prior use is usually not a problem, since it was almost certainly cooked previously; it’s unlikely that uncooked solids would be found on a ladle. However, if there is cold liquid on the ladle from a previous use, even if it was originally hot but has now completely cooled off, it should be wiped dry before putting it back into a pot that has hot food in it. If the liquid is still slightly warm, there is no need to wipe it dry before putting it back into the pot.
See here in the מראי מקומות section for elaboration on the matter.