607. It's Not About Cooking

Shabbos 3:16

Meat, onions and eggs may not be roasted over a fire unless they can be roasted sufficiently before Shabbos that they would be fit to eat. If this is the case, they may be left on the fire to roast more on Shabbos. This is because increasing the heat would prove detrimental: if one stoked the coals, the food would burn. This is also why incense may be left to perfume clothes before Shabbos starts; because if one were to stoke the coals, the incense would burn and the smoke would ruin the clothes.

Shabbos 3:17

From the past few halachos, we can see that the prohibitions in this area are not because the food finishes cooking on Shabbos. Rather, they are rabbinic laws passed to keep a person from stoking the coals. Therefore, wool may not be put into the dye vat prior to Shabbos unless it is removed from the fire out of concern that one may come to stoke the coals. Also, the vat should be sealed with clay so that one will not come to stir the dye once Shabbos begins.