The cooling fan will not shut off. The engine is not over heating

How long does it run? some cars will run the fan for a few minutes to ensure that too much heat does not build up under the hood. Wait for 5 minutes and see if it is still running when the engine is off. If it is you may have a bad temperature sensor. Does the engine temperature gauge work properly?

This sounds like the heat sensor in the engine cooling system is failing/has failed completely (internal switching contact remains closed). The engine cooling fan should only come on at the prescribed heat temperature but will also remain active after shutting the engine down, if the engine temp is still above the prescribed temp. Regarding the A/C fan, this is most likely a wiring fault, possibly a short circuit with the car's ignition circuit.

It can be faulty fan relay.The relay is not turning the system off.Or its wire short issue.Even with ignition off ,the fan relay is getting power so its not letting the fan to turn off.Bypass the fan control relay and see if still the fan works with ignition off or not.

For more troubleshooting check the link below:------

Cooling Fan Stays ON with Ignition Off?

http://whatisbyme.blogspot.in/2012/07/cooling-fan-stays-on-with-ignition-off.html
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Cooling fan relays location ?

http://technoanswers.blogspot.in/2012/02/cooling-fan-relays-location-on-1998.html
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DIC says "COOLING FAN FAULT"?

http://schematicsdiagram.blogspot.com/2011/12/dic-says-cooling-fan-fault.html
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Heater fan and headlights will not turn off with ignition off?

http://technoanswers.blogspot.com/2012/01/heater-fan-and-headlights-will-not-turn.html

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Fuel pump relay and cooling fan relay troubleshooting ?

http://repairhelpcenter.blogspot.com/2011/10/fuel-pump-relay-and-cooling-fan-relay.html

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Where Is Radiator Fan relay and Fuse Located?

http://schematicsdiagram.blogspot.com/2011/12/where-is-radiator-fan-relay-and-fuse.html

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These will help.
Thanks.

There are two fan switches on that car;
The main one turns the fan on and off when the ignition is on and the car is running.
The second switch powers the fan if the ignition is off and the engine temperature is too high, to cool the engine off if it was just shut down.
It sounds like your main fan switch has gone bad and needs to be replaced since it's not sending any signal to the fan, while the engine is running.

Should be a relay somewhere in the engine compartment - may be failing. You may be able to switch with another relay to diagnose.
Check your owners manual under fuses and relays.

That is what it is supposed to do. There is a temperature switch that opens and closes as the coolant reaches certain temps. When it reads those temps it turns the fans on or off as needed. Your fan circuit is separate from your ignition to allow it to keep the engine cooled down after you shut the car off. This prevents possible damage to the engine due to heat. Today's engine have a lot more aluminum in them and it is affected by heat more so than the old cast iron engines. It is more noticable in warm weather because things heat faster and cool slower. Unless the fans run steady or not at all, you should be okay. Turning on the A/C will turn them on quicker and longer because it makes the engine work a lot harder. Hope this helps.

Odds are your electric cooling fan[s] isn't coming on. This fan should only run when the a/c is on or when the engine temperature has reached about 218 degrees. Once the a/c is off or the engine temp drops to about 210 degrees it shuts back off again. It rarely comes on at speeds over about 35 mph because at that speed enough air is forced through the radiator to keep the engine at about 198 degrees. I would start by looking for a blown 30 amp fuse under the hood. There may be two of them marked "Cooling fan 1" and "Cooling fan 2" or something similar. If the fuses are good you could have a faulty cooling fan motor that just isn't running. Hope this helps a bit!

the coolings fans are designed to run for a little while to dispense heat they dont do it all the time turn usually during higher hot days w/ac on or higher hot days goes off automatically

You are talking about the thermo electric cooling fan, its operation is independent of the car's electical system. It is switched on and off by the engine temperature. When you park, the engine heat soaks upward to heat the thermostat turning the fan on. It will run until the engine cools down and the thermostat switches it off. Quite normal operation.

You most likely have air in the cooling system.You would need to bleed the cooling system of air.There should have bleed screws near water neck,or thermostat.Do this cold.Remove the radiator cap and fill full.Then start the engine and loosen the screws and watch for nothing but coolant to flow out(no air or bubbles).When you are sure the air is gone out of the cooling system,shut the bleeder screw off,and fill radiator up and test to see that engine runs cool,and you have heat at all speeds and rpm s.The electric cooling fan should come on at a tempuratue of about 215 or so.But just as important,the cooling fan should cut off at a lower tempurature.If the cooling fan does not do this,you still have air in the system.If you can not get the air out this way,then do this.Remove the radiator cap and reservoir cap and fill them both up full.The reservoir needs to be over the fill mark a good deal.Replace the caps.Start the engine with ac and heat off.Let it run until the engine gets to about 212 or 215 degrees and shut the engine off.Wait about 30 minutes and check the reservoir to see if the coolant has dropped.It should have dropped.If the reservoir has dropped or not ,do this again and again untill the reservoir drops in coolant level,and engine temp is good(fan goes on and goes off).Remember to refill the reservoir as needed as it drops,not to run out of coolant.