The primary driver for your respiratory rate is the pH of your blood. For instance, metabolic disorders that result in a drop in blood pH will result in an incr

The primary driver for your respiratory rate is the pH of your blood. For instance, metabolic disorders that result in a drop in blood pH will result in an increase in respiratory rate/depth (e.g. Kussmaul breathing). As far as I know (with a fairly deep anatomy and physiology background) there is no mechanism by which body temperature can directly influence respiratory rate. If your respiratory rate increased just to get rid of heat, you’d also be blowing off more carbon dioxide and would end up in a state of respiratory alkalosis. As you mentioned, sweat is also evaporating water, and that is a much more effective way of dumping heat.