According to SA (451:6), if a utensil was sometimes used as a kli rishon and other times as kli sheni it is koshered based on majority usage. Thus, if it was used primarily as a kli sheni, it can be koshered like a kli sheni. Likewise, if it was sometimes used in fire, but primarily used as a kli rishon, it may be koshered in a kli rishon. And if it was sometimes used as a kli rishon, but primarily used cold, it can be koshered in cold water. According to Rema, on the other hand, the utensil must be koshered based upon its most intense usage, not according to its predominant use.
To illustrate, if a particular spoon is usually used to eat soup from a kli sheni, and occasionally used to stir food in a pot on the fire, Shulĥan Arukh maintains that it is koshered based on its primary usage, which in this case would mean hagala in a kli sheni, whereas according to Rema it must be koshered via hagala in a kli rishon, in keeping with its more intense form of absorption.
Rema’s rationale is that once the utensil has absorbed the taste of foods in a more intense fashion, the only way to remove what has been absorbed is by koshering the utensil with the same intensity. Shulĥan Arukh’s opinion is based upon the presumption that the koshering of the utensil takes place more than twenty-four hours after its last use, at which point the absorbed taste is foul. According to the Torah, such a utensil does not require hagala. The Sages, however, required that any utensil that has absorbed the taste of forbidden food be koshered, out of concern that if they were to permit the use of such utensils after twenty-four hours had elapsed, people might misjudge the time and inadvertently treat leniently utensils that had been used in the past twenty-four hours. But the Sages required that such utensils be koshered according to their common use, and not their most intense use.
In practice, the custom le-khatĥila is to be stringent and to kosher every utensil according to its most intense usage. Furthermore, even if a utensil’s most intense usage was irui, the custom today is to kosher all utensils in a kli rishon on a flame, in order to avoid a situation in which one has forgotten that a utensil was in fact used as a kli rishon on a flame. However, in extenuating circumstances, one may be lenient and kosher a utensil according to its primary use (MB 451:47; Kaf Ha-ĥayim ad loc. 100).
If a utensil was used primarily as a kli rishon and occasionally on the fire, even Rema allows koshering via light libun (MB ad loc. 48). If there is a concern that even light libun will damage the utensil, it is considered a be-di’avad situation, and one may kosher it in a kli rishon, in accordance with its primary use (Kaf Ha-ĥayim ad loc. 108).