At what temperature would you stop cooling down a person that has had heat stroke or heat exhaustion?

Normal body temp: The point of cooling the body in heat stroke is to bring CORE temperature back to about normal body temperature, which is 98.6 deg F plus or minus 2 degrees (or 35 to 37 deg C, approximately). You're never going to get it perfect, but the point is to try to get somewhere near "normal" & then allow the body to heal itself. Drink plenty of fluids & rest if you have heat exhaustion. TTYD or HT Prime.