The fans only run when the engine reaches 212 degrees, and they turn off at 198 degrees. A quick test to see if the entire system is working is to unplug the two-wire coolant temperature sensor. There's a different one with only one wire for the dash gauge. The two-wire sensor is for the Engine Computer.
When you unplug the sensor, the Engine Computer will turn on the radiator fan relay just in case the engine is overheating. The Check Engine light will turn on too and a fault code will be stored in the computer. The light will go off after you restart the engine, and the code will erase after about 50 engine starts.