Yeah, but the question rather is, would let's say 32°C water, 5°C temperature gradient, work to cool the body, if completely submerged? When ambient conditions

Yeah, but the question rather is, would let's say 32°C water, 5°C temperature gradient, work to cool the body, if completely submerged? When ambient conditions are deadly wet-bulb 32°C, would it still cool the water to its original 32°C? So, my thinking would be, if the heat transfer from the body to the water and from water to air (through large surface) is sufficient. In a shaded pool, so all heat transfer from the outside is by convection and conduction. I guess, if it would be sufficient cooling, you could also "just" drink the water and remove hot sweat from the skin, or dispose urine, instead. In theory, never mind electrolytes.