Tosafos discusses whether one is allowed to leave a pot with raw apples cooking on a fire before shabbos. Tosafos suggests that since one is allowed to do shehiya and leave a pot cooking on a fire once it is a third of the way cooked, כמאכל בן דרוסאי, without a concern that he will stir the flames, one can also leave the pot with apples cooking since it is even more edible than food which has reached מאכל בן דרוסאי.
It is possible that the rationale of Tosafos is that just as when something reaches כמאכל בן דרוסאי it is considered cooked and therefore we aren't concerned that he will stir the coals to cook it more, similarly something that is edible without being cooked is considered halachically cooked so that the stirring of the coals is not a concern. However, this clearly isn't the opinion of Tosafos. In the very next discussion Tosafos forbids one to wrap on shabbos the pot containing the apples because it would be a violation of cooking. Tosafos clearly considers there to be a violation of cooking even on food that is edible without cooking. Therefore, when Tosafos permits shehiya on the pot containing the apples, their rationale is that although we don't consider it cooked, he won't be motivated to stir the coals since he doesn't care that much about it being cooked. This is to the exclusion of the opinion of the Rambam (9:3) who holds that there is no Torah prohibition to cook things which are edible raw.
Rav Moshe (Dibros, # 4) points out that according to this approach we can prove from Tosafos that they do not consider כמאכל בן דרוסאי to be considered cooked. Had Tosafos held that כמאכל בן דרוסאי is considered cooked on a Torah level so that any further cooking wouldn't constitute a violation, there would be no similarity or proof from מאכל בן דרוסאי to a food edible raw since Tosafos clearly holds that by a food edible raw there is a violation of cooking. How then can Tosafos prove that we can leave the pot of apples on the fire from the right to leave the pot that has been cooked כמאכל בן דרוסאי on the fire; perhaps we only permit כמאכל בן דרוסאי because it is considered already cooked. Clearly, Tosafos must be assuming that there would be a violation of cooking both by a food edible raw and by a food that is כמאכל בן דרוסאי, therefore just as by מאכל בן דרוסאי we aren't concerned that he will stir the coals, the same will be true with a food that has already been cooked. Based on this, Rav Moshe points out that Tosafos here contradicts Tosafos at the beginning of perek kirah who holds that once something is כמאכל בן דרוסאי it is considered cooked m'doraysa and there wouldn't be any torah violation in cooking it more.
Tosafos writes (end of d.h. mai) that we do not permit someone to place a kettle of water in a place where it can reach a temperature of yad soledes bo, even if their intent is to remove the kettle from being near a heat source prior to it reaching the temperature of yad soledes. However, in the question when Tosafos suggests this distinction, rather than using the term דלמא משתלי - lest one forget, Tosafos uses the phrase דשמא יבא לטעות ויניח שם עד שיתבשל. The Eglei Tal asks on Tosafos why are we concerned when someone puts a kettle of water near the fire where it can potentially reach yad soledes out of fear that he may forget; forgetting would not qualify as a מלאכת מחשבת and it wouldn't be an issur d'oraysa so why should we make a gezeira that he may forget since even if he does it will only be an issur d'rabonon? It seems to me that the way Tosafos articulated the concern in the question, avoids the question of the Eglei Tal. If one would forget the pot of water on the fire and it would reach yad soledes, the inadvertent act of cooking would not qualify as a מלאכת מחשבת and it would not be an issur d'oraysa. That is why Tosafos at first doesn't say that one may forget it, rather that one would make a mistake and leave it there. Perhaps Tosafos is trying to say that we are not concerned for him forgetting, rather we are concerned that he will make a mistake in halacha and think that it is permissible to leave it to heat up even if it is not on the fire. A mistake in halacha would certainly qualify as a מלאכת מחשבת and constitute an issur d'oraysa.
Rav Moshe approaches Tosafos from the exact opposite perspective of the Eglei Tal. Rav Moshe (Dibros #5) asks, why is Tosafos only concerned that he may forget the pot or come to make a mistake, implying that the entire problem with placing the pot near the fire when he intends to remove it is only a Rabbinic violation and not a Torah violation. Rav Moshe asks that given the nature of the melacha of cooking, it is similar to planting. The issur is violated by setting up a situation where something can cook. The requirement to actually cook is merely a condition, so that if it somehow is removed prematurely the person would retroactively not have violated the issur. However, if they would "forget" it there, even though it is completely inadvertent, they would be in violation of a Torah prohibition of cooking. Therefore, even if we weren't concerned that he would actually forget the pot near the fire, we couldn't permit doing an act that is an issur d'oraysa just because he plans on making sure the condition isn't fulfilled. Rashi 40b implies that one can actually leave water near a fire to remove the chill so long as he plans on removing it before it reaches yad soledes. Rav Moshe's asks that Rashi implies that it isn't even an issur d'rabonon, but really it should even be an issur d'oraysa!