2011 chevy equinox warning screen that a/c will not run because engine too hot, engine fan stays on after i shut the car off, temp gauge stays at cold-doesn't move, freezing cold out. coolant and

So....is it running hot?....What does the temp guage say?....
This could be a number of different things..I wonder if the cooling fans are comming on?...I wonder if the radiator is flowing properly...Maybe the coolant temp switch is faulty...You prob need to take this to a qualified automotive repair shop to have some of these questions answered?

Could be temperature sensor if car is not overheating.
make sure your coolant level is good.
Just to make sure you know this. The radiator fan is activated by the coolant temp in engine. The radiator fan can come on even if the car is turned off.
Something I would check first. Look at the radiator fans. If you have 2 one will come on and off with the A/C. The other will come on when the engine gets to operating temperature. As long as the engine temp is in normal range the engine fan should stay on. When temp seems to rise above normal make sure the fan is running.
I had a issue years ago where the fan relay would get very hot(hot compared to the other relays) and would open and the fan would go off. When the relay cooled down it would close and the fan would run again. I fixed by changing the relay.

You maybe low on coolant. Also have the computer codes checked. Many auto supply places do this for free.

Not exactly.
The check gauge warning light is on because the temp gauge is reading hot.
Does the temp gauge read hot as soon as you turn the key switch on, or not until the engine as run for a few minutes ?
If it reads hot without the engine being started, there may be a short in the wiring or the sensor may have failed.

Yes it may be the wires are shorting or its actually the problem with instrument cluster.
Also get the vehicle scanned for any error codes stored in computer this will confirm whether is short circuit issue or actual problem:------
I suggest you few help links with accurate solutions to refer/go through:----Click the link below:------

Battery and brake Warning lights on Dash
http://alltypesofpartsreplacing.blogspot.com/2012/10/battery-and-brake-warning-lights-on-dash.html
--------------2002 Ford Windstar: Brake Warning Light ON dash? http://schematicsdiagram.blogspot.in/2012/06/2002-ford-windstar-brake-warning-light.html
-------------ABS & Brake warning lights remains steady on dash? http://schematicsdiagram.blogspot.com/2011/12/abs-brake-warning-lights-remains-steady.html
-----------Chevrolet Tahoe Hood open warning on dash and alarm sounds? http://schematicsdiagram.blogspot.com/2011/12/chevrolet-tahoe-hood-open-warning-on.html
-----------2005 Chevy Impala: Service Vehicle Soon Warning Light? http://whoisbyme.blogspot.in/2012/06/2005-chevy-impala-service-vehicle-soon.html -------------- Malfunction Indicator Light ON http://whoisbyme.blogspot.in/2012/06/malfunction-indicator-light-on.html
-----------Car Runs Fine But Check Engine light is ON?

http://whatisbyme.blogspot.in/2012/05/car-runs-fine-but-check-engine-light-is.html

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Check engine light with codes P2195 and P2197?

http://howtobyme.blogspot.in/2012/01/check-engine-light-with-codes-p2195-and.html

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How to Read Codes from Check Engine Light? http://schematicsdiagram.blogspot.com/2011/12/how-to-read-codes-from-check-engine.html
-------------These will help.Thanks.

Its normal for a fan to run after the engine is shut off if the temperature is high enough,but if your car is running hot,you have other issues

For car running hot and overheating issues, I suggest to you go through this help links. Click this link below and go through the troubleshooting procedure to take care of the problems: ----Car runs hot? http://howtobyme.blogspot.com/2011/11/car-runs-hot-in-traffic.html
-----------All types of car overheating problems and troubleshooting?

http://technoanswers.blogspot.com/2011/11/all-types-of-car-overheating-problems.html
Car freeze overnight and started overheating while driving?http://technoanswers.blogspot.com/2012/01/car-freeze-overnight-and-started.html-----------Engine Overheats and heater blowing cold?

http://howtobyme.blogspot.com/2011/11/engine-overheats-and-heater-blowing.html

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Car overheats and Air blows hot at idle?
http://howtobyme.blogspot.com/2011/11/car-overheats-and-air-blows-hot-at-idle.html
--------overheating? http://schematicsdiagram.blogspot.com/2011/12/buick-century-overheating.html
----------Car engine Overheats and transmission starts slipping?http://schematicsdiagram.blogspot.com/2011/12/car-engine-overheats-and-transmission.html
----------This details will help.Thanks.

For car running hot and overheating issues, I suggest to you go through this help links. Click this link below and go through the troubleshooting procedure to take care of the problems: ----

temp gauge goes erratic? http://technoanswers.blogspot.com/2012/01/heater-blows-intermittently-and-temp.html

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Temperature gauge keeps fluctuating up and down close to red? http://technoanswers.blogspot.com/2012/01/temperature-gauge-keeps-fluctuating-up.html

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Car runs hot? http://howtobyme.blogspot.com/2011/11/car-runs-hot-in-traffic.html
-----------All types of car overheating problems and troubleshooting?

http://technoanswers.blogspot.com/2011/11/all-types-of-car-overheating-problems.html
Car freeze overnight and started overheating while driving?http://technoanswers.blogspot.com/2012/01/car-freeze-overnight-and-started.html-----------Engine Overheats and heater blowing cold?

http://howtobyme.blogspot.com/2011/11/engine-overheats-and-heater-blowing.html

---------------------------

Car overheats and Air blows hot at idle?
http://howtobyme.blogspot.com/2011/11/car-overheats-and-air-blows-hot-at-idle.html
--------overheating? http://schematicsdiagram.blogspot.com/2011/12/buick-century-overheating.html
----------Car engine Overheats and transmission starts slipping?http://schematicsdiagram.blogspot.com/2011/12/car-engine-overheats-and-transmission.html
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Temperature gauge does not move and no heat when heater is ON? http://technoanswers.blogspot.com/2012/01/temperature-gauge-does-not-move-and-no.html

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This details will help.Thanks.

Should be located on the lower intake on right or left toward the front. Two wires watch cause there's and air temp that might look the same.

check the coolant temp sensor