I feel sick and exhausted when I run in heat. Alternatives?

Heat stroke. Best solution might be to run in a cooler climate or run indoors on a treadmill. Pushing yourself in this environment may put you at risk for heat stroke, a dangerous emergency.
Fluids. The short answer is to take plenty of fluids with you. Heat exhaustion happens when you deplete your fluid and electrolytes, so bringing a fluid pack helps a lot. You should also wear light colored clothing. Over time, your body does adapt as well.