yad soledet bo

Question

When worrying about a food's having reached that temperature (whether for bishul, ta'am, returning food to a fire or what not) where would one measure? Food cooks unevenly and the outside might be yad soledet while the inside is barely warmed up. Does the entire food have to be at this temperature? Does just the kli holding it even if the food is not that hot? Thank you.