Same way you'd treat hyperthermia:
Advice from: https://www.ncbi.nlm.nih.gov/books/NBK459311/
- Cold bath
- Saline IV (You don't need gunpowder to make hypodermic needl es and a 0.9% salt water mix)
- Ice packs
- Wet Sheets/towels.
- Fan
- Water spray bottle
You said this was for emergency use only, so it probably doesn't need purpose built device. But if this is common, you could make a crude gravity fed misting spray.
Pour water in a funnel upstairs, water flows down a tube, hits a nozzle, and sprays fine water. Water hits the hot person, and evaporates. Combine with someone waving a hand-held fan at them (or placing them in a breeze caused by passive ventilation design), one could easily cool down.