The idea that you'll get cramps from cold water is a myth. Drinking water, whether it's warm or cold, before or during running should not cause side stitches. The best ways to prevent side stitches while running is to make sure you warm-up properly and to breathe deeply through your mouth. If you avoid drinking during runs because you're worried about cramps, you could end up with much bigger problems, such as dehydration.
When it comes to drinking during runs, cold water is better than lukewarm water because it's more quickly absorbed in the body. Drinking cold water during a hot run also makes you feel cooler. (I know this isn't news to anyone who has been forced to gulp warm water during a race or run!) But the effect is not just psychological. The cold water also produces a slight physiological cooling effect.
Of course, it's not easy to keep your water cold during outdoor runs in the heat. It helps to use a hand-held water bottle with an insulated cover so the warmth from your hands doesn't immediately warm up the water. You can also put ice in your water bottle or partially freeze your water bottle before your runs, which helps keeps your water cold for longer.