The Huffington Post explains that people get flushed or red in the face because during exercise, capillaries in the face and body dilate to move heat to the skin's surface so it can be radiated off. This process helps keep the body cool while exercising.
According to the Huffington Post, some people become redder in the face because they experience more significant dilation of the capillaries. More prolonged dilation causes the face to stay red for a longer period of time.
In extreme heat, a red face may be an early indication of heatstroke. If a red face is accompanied by excessive sweating, nausea and lightheadedness, stop exercising and call a doctor.