Heat stroke is a very serious condition. Having a headache, thirst, being very hot and sweaty does NOT mean you have heat stroke. Yes these are symptoms of heat stroke, but if you only have these symptoms you do not have heat stroke.
I actually did have heat stroke in Italy. I was very red, but no longer felt hot at all. My heart rate went way up as did my core temperature.
Heat stroke is dangerous. If you really think your kids have heat stroke, seek medical attention. But usually the term is not used to mean that. A but like cold and flu. And yes it annoys me.