99 Cavalier overheating

My 99 Cavalier 2.2L was overheating. I checked the fan and it worked when I hooked it directly to the battery, so I changed the relay switch and the fan worked when I turned the a/c on. But it still overheats when the a/c is off. I know that there is a temperature sensor, but I don't know if this switches on the radiator fan.
Is there another fan switch that I don't know about?
Is there anything else that can cause this?