The coolant light comes on even tho the coolant is full could it be the fan

Check the coolant level.
The radiator must be full, coolant should be mix of 50/50.
If it is full, and stays full when overheating, the most common cause is a defective cooling fan.
One of your electric radiator fans is for your A/C and one is for the radiator cooling
Any time the temperature gauge/ or red light comes on, that fan should be running.
Raise the hood and look the next time it overheats, and if no fans are running, you need get it fixed quick, lest you blow a head gasket.
The problem could be either the electric fan motor, or the sensor switch that screws into the engine block.
If the coolant stays full, and the fans are running, you may have a stuck or closed thermostat.
God bless your efforts.

Well the light staying on could be a short in the wiring or a failed temp switch. And that could affect the radiator fan but I doubt it.
Have you checked the water pump and thermostat ? Is coolant flowing in the system ?

have you checked the fuse and also the relay.

IF COOLANT TEMPERATURE RISING,CHECK TOP RADIATOR HOSE IF TOP RADIATOR HOSE IS NOT HOT REPLACE THERMOSTAT AND RADIATOR PRESSURE CAP.IF ALL IS GOOD.IF CAR OVERHEAT WHILE SITTING IN A LONG TRAFFIC LINE.THE COOLING FANS NOT WORKING,CHECK COOLANT FANS FUSE AND RELAYS.IF BOTH IS GOOD.HOT WIRE TO SEE IF COOLANT FAN TURNS ON IF NO FAN MOTOR BAD.IF YES FAN MOTOR GOOD. PROBLEM COULD BE FAULTY COOLING FAN WIRING OR BAD ENGINE COOLANT TEMPERATURE SENSOR BAD OR FAULT IN THE PCM.

SOUND LIKE ENGINE OVERHEATING,CHECK COOLANT LEVEL MAKE SURE YOUR RADIATOR FULL OF ANTIFREEZE.IF YOUR COOLANT OVERFLOW JUG IS EMPTY COOLANT LEVEL IS LOW.NEED ADD MORE COOLANT TO OVERFLOW UNTIL COOLANT STAY AT FULL COLD MARK. DONT OVER FILL COOLANT OVER FLOW JUG.IF COOLANT OKAY ENGINE OVERHEATING REPLACE THERMOSTAT.MAKE SURE ENGINE COOLING FAN IS WORKING IF YOU COME TO A STOP CAR SITS FOR A LITTLE WHILE START OVERHEATING THE COOLING FAN NOT TURNING ON , BECAUSE COOLANT FAN FUSE BLOWED OR YOU HAVE BAD RELAY,THE ENGINE COOLANT TEMPERATURE SENSOR FAULTY.IF YOU HAVE THE CLUTCH TYPE COOLING FAN, MAKE SURE WHEN TURNING CLUTCH FAN WITH HAND COOLING FAN SHOULD HAVE RESISTANCE WHEN HOT.IF CLUTCH FAN FEEL WOBBLY AND LOOSE REPLACE IT.TAKE VECHICLE TO AUTO ZONE OR ADVANCE AUTO PARTS OR ANY AUTO PARTS STORES THEY WILL CODE SCAN CAR FREE AND GIVE YOU THE CHECK ENGINE LIGHT TROUBLE CODE TO SEE WHAT CAUSING CHECK ENGINE LIGHT TO TURN ON.

On the end tank of the radiator,pass side,there is a sensor for that.It's not a float or anything ,it's
electronic,SOMTIMES you can just tap on them and they come to life ,for awhile.
If not the sensor is easy to change,seemed like they are like 30 bucks tho.

ok this might sound crazy but you say you smell coolant but never said if you checked to see if it was full posible bad coolant temp sensor or no coolant passing the sensor please more info on coolant usually if low coolant fan will stay on however you say you smell coolant. If the coolant sensor is bad fan wont command on it will have a high resistance a low coolant temps and low at high temps. I would check sensor since its obviously getting hotter than half way if you dont have coolant leak the relay behind the head light by the way is a common problem I would have just changed it if its original and it grounds to body thats why it is riveted however you can bolt them. Hope this helps check for thermostat opening at right temps to.

The low coolant light may be due to the sensor, these sensors go bad often, they are located on the front side of radiator. as far as overheating the first then i would do is a block test, this is done with a fluid to test if exhaust is entering the cooling system and stopping the flow which make it overheat, if it passes this test then i would replace the thermostant and go from there, hope this helps.

On a water cooled engine... the impeller on the water pump is no longer working correctly. It has probably come loose from the input shaft and is no longer pumping water. You can prove this on a warm engine by filling the radiator to the top and then accelerating / decelerating the engine... if you don't get a change in the water level the water pump is shot.

Kelly

FAULTY THERASTATE OR HEAD GASKET GOING