Warm water opens pores and cold water closes them. Depending on the severity of the rash, water temperature can either soothe or aggravate the skin condition by spreading or calming it.
Warm water creates steam to open pores. Sweating is an example of this. Water higher than body temperature helps to flush out impurities. Taking a bath in it can help to cleanse away the rash temporarily. Hotter water also relaxes the skin, much like a sauna does.
Cold water in return closes pores. Many argue that cold baths have health benefits. Women's Healthcare claims that cold water "can temporarily alleviate skin irritations such as insect bites and minor skin allergies." Warm water also causes particles to expand, while cold water shrinks them, perhaps ceasing the rash.
There have been many debates on the healing properties of oatmeal. Granny Med agrees that oatmeal "binds to the skin, sealing in moisture and softening... it also soothes and protects the skin, bringing relief to the itch." Dissolve oats into hot water to penetrate the rash, then rinse with cold water to calm the distressed skin.