A normal healthy person not on meds that cause trouble in the heat can take pretty extreme temps if they stay hydrated and keep their electolites up. Modern folks do this with sport drinks, but we all know this ain't period correct.
So I'll offer the PC fix for this. It's called several names and recipes vary, Switchel, also switzel, swizzle, ginger-water, haymaker's punch or switchy and who knows what else.
8 cups barley water. (Boil 1 pound of barley in the water and eat the barley for breakfast with milk and sugar)
1 1/2 cups molasses
1 cup apple cider vinegar
1 tablespoon of salt
1 1/2 teaspoons ground ginger.
Heat water and dissolve all the ing chill, serve cool but not cold. (Cold drinks will cool your core to much and the body has to work to warm it up.)
Wear loose fitting cotton clothing and keep as much skin covered to avoid exposure to the sun which will heat the body up also.