DON'T DO IT!
Dehydration hurts your performance, and slows your ability to recover for the next workout. Continuing to run when dehydrated can lead to heat stroke and death.
To better understand the dangers of dehydration, let's take a look at what happens in the body when you run on a warm day. First, your body automatically sends more blood to the skin for evaporative cooling, leaving less oxygen-rich blood going to your leg muscles.
Second, the warmer it is, the more you sweat, and the more your blood volume decreases. Less blood returns to your heart, so it pumps less blood per contraction. Your heart rate must increase, therefore, to pump the same amount of blood. The result is that you cannot maintain as fast a pace on a warm day.
Worst of all, dehydration tends to catch you unawares. If you replace a little less fluid than you lose each day, after a few days you will run poorly but may not know why. Exercise physiologist and marathoner Larry Armstrong, Ph.D., induced dehydration equal to 2% of body weight in runners and observed a 6% decrease in speed over 5K or 10K. That's a 3% decline in performance for each 1% decrease in bodyweight due to dehydration.
It is not unusual to lose 3-4 pounds of water per hour when running on a warm day. At this rate, after 2 hours a 150 pound runner would lose 6-8 pounds, representing a 4-5% loss in bodyweight and a 10-15% decrement in performance. That's about an extra 1 minute per mile. Losing more than 4-5% of your bodyweight, however, could do even more serious damage to your body.