During which heat emergency do you cool the casualty's body by sprinkling him or her with water?

In cases of heat exhaustion, cooling the casualty's body can be effectively achieved by sprinkling them with water. Heat exhaustion occurs when the body loses an excessive amount of water and salt, usually through sweating. This condition is characterized by symptoms such as heavy sweating, weakness, dizziness, and nausea.

By applying water, especially if shaded and combined with air movement, the evaporation helps lower the body temperature, which is critical in preventing the condition from progressing to heatstroke. Heat stroke is a more severe heat-related illness where the body loses the ability to regulate its temperature, and aggressive cooling methods, such as immersion in cold water, are typically required rather than just sprinkling.

Heat cramps and heat fatigue, while related to heat exposure, do not primarily require cooling methods like sprinkling with water as part of their initial treatment. Heat cramps involve muscle spasms due to dehydration and can be addressed with hydration and electrolyte replacement. Heat fatigue is often characterized by feelings of tiredness and may not necessitate immediate cooling interventions like those used in heat exhaustion.

Thus, targeting cooling through water application is specifically suited for cases of heat exhaustion, making it the correct answer.