Yes throwing up is one of the signs and symptoms of a person experiencing heat exhaustion.
Other signs and symptoms of a person experiencing heat exhaustion are, muscle cramps, diarrhea, nausea and dehydration.
If a person is experiencing vomiting or any of the other symptoms then the heat exhaustion is most likely severe and you should go to the emergency room or get an ambulance on the way since heat exhaustion can be deadly or even cause a stroke.