AS a Physical Educator, former competitor ,and lifelong swim instructor.
Through theory and experience, I believe that someone does in fact sweat while swimming, and, the temp. of the water does not matter. It depends on the intensity of the swimming effort. If the intensity
is strong enough, the body's internal temp. will rise, as a response, sweat will be produced. It will be washed away while in the water. but. if someone exits the water immediately after swimming. and if the
humidity is high enough, they will continue to sweat until the body cools down.