This is a question that is asked all the time. To answer this question it is important to know what each does.

Heat causes relaxation by lengthening the muscle fibers. You can use heat if your muscles are tense. I don't recommended heat for new injuries, because injuries cause an inflammatory response in the joint and surrounding muscle tissue. Heat is like adding gasoline to the fire. It may feel good temporarily in a new injury, but it will delay healing time and could cause further injury.

Ice reduces the inflammation in a new injury sprain/strain. It also reduces swelling by limiting blood flow in the area. That is why it is best to use ice only for the first 48 hours. Use an icepack for 10-15 minute durations and not directly on the skin, but through a thin towel. The method of applying icepacks for short durations then reapplying will give you maximum benefit for a sprain/strain injury.