1. Shmuel: One may extinguish a metal coal that is in the public domain so that it should not cause harm.
2. Similarly, one may carry a dangerous thorn out of the public domain to the side of the public domain in increments of less than four Amos at a time.
3. The Gemara discusses mixing hot and cold water on Shabbos for the purpose of drinking.
4. The Beraisa explains that the law is different for mixing hot and cold water in a bathtub for bathing.
5. The Mishnah says that one may not put spices in a hot pot that was just taken off the fire.
A BIT MORE
1. However, one may not extinguish a burning piece of wood, because such an act may constitute a Torah prohibition.
2. If the thorn is in a Karmelis, one may carry it normally to the side of the Karmelis where it will not cause any damage.
3. Beis Shamai: One may pour hot water into a cup of cold water, but not cold water into a cup of hot water. Beis Hillel: Both are permitted.
4. Even Beis Hillel admits that one is allowed only to pour hot water into cold water, and not cold water into hot water. Rebbi Shimon ben Menasya forbids even pouring hot water into cold water for bathing.
5. However, one is allowed to put spices on food that is in a plate or serving bowl after it has been transferred from the pot in which it was cooked on the fire.