The efficiency of sweating depends on rel. humidity. Not what's being discussed here.
The fact that increasing airflow will increase the rate at which you heat up (and how much heat your body must shed) if that airflow is hotter than your core body temperature is just physics 101. Why do you think fan-forced ovens have lower cooking times or temperatures in recipes?
The minimum temperature to which you can evaporatively cool something also depends on humidity. If evaporation is still doing anything (i.e. wet-bulb temperature does not exceed body temperature, in this context), increased airflow will absolutely still have a cooling effect.
