I really don't know why the body does not sweat at times when exerted. I have found since i became hypothyroid I am cold at the time and when I do exercise I won't sweat either.
I think it can be many things to check out - hormonal imbalances can trigger situations.
No sweat calls anhidrosis, so first you should go to a Dermatologist to see if you have a problem with the eccrine glands (no sweat glands, sweat glands malfunction, etc) and the doctor probably will ask for some specific tests you should do for the right diagnosis (of Anhidrosis) . Treatment of anhidrosis involves addressing the underlying cause (hypothyroidism , autoimmune disease (sjogren's), diabetes, metabolic disorder, skin damage, genetic factors, nerve damage, etc)