To amplify a bit, if it only has one fan then the fan will be a 2 speed fan, it should run on high when the AC is on max. If the AC is off and then engine reaches operating temp then it will be commanded to run in low speed initially and then high speed if needed.With the AC off the fan will not kick in, you need to check your fan. Start your car and turn the AC on and see if the fan kicks on. The fan is supposed to turn on when the AC is put on.
If it has 2 fans, then one is typically for the radiator and the other runs when the AC is on but both can run is conditions are hot enough.