1999 Toyota Tercel - about 140,000 milles - 4 cylinders

My problem is that the radiator fan doesn't work when the thermometer sign reflects high temperature. When I turn on the A/C both fans works, but the temperature indicator doesn't reduce the temperature.

I always check the water from the radiator and it is full. What can be the problem? Some sensor or water pump, what I have to check. Thanks