Fill a teakettle with 4 cups of cold water. Place the teakettle on a stove top, and bring the water to a boil over high heat.
Place the pot that has burnt tomato soup on its bottom in a sink by itself. Pour the hot water into the bottom of the pot slowly. Cover the pot with a tight-fitting top, and let the pot sit in the sink for 60 minutes or until the water is cool enough to handle.
Pour the water out of the pot, and wash the pot with a soft sponge and mild dish soap. Dry the pot with a clean kitchen towel or paper towels to see if all of the burnt-on tomato soup was removed.
Repeat the process once if any bits of tomato soup remain in the pot.
Put the pot on a stove top, and pour water and 1/2 cup white vinegar into the pot. Stir the water and vinegar with a wooden spoon to combine them.
Cover the pot with a tight-fitting top, and bring the water and vinegar mixture to a boil. Boil the liquid over high heat for 20 minutes.
Pour the water and vinegar mixture out of the pot into a sink. Wash the pot with a soft sponge and mild dish soap to remove remaining food.
Dry the pot with a clean kitchen towel or paper towels. Repeat the process if food remains on or in the pot.