I have a 2008 Malibu LS, 4 cylinder.My engine light has been on and at the same time my temperature gage does not work and the fan keeps running, then the engine light went out for a couple of days, the temperature gage worked, but sometime the engine light was off and the temperature gage still worked. The temperature gage can be working and you are driving and all of a sudden it stops working. Someonoe suggested a sensor. Does anyone know what kind of sensor and where and how hard is it to change this yourself?

Did it run okay after the starter was changed? There are lots of ideas in the link, but really, you need a mobile auto-electrician with a pro grade scan tool computer to check for Diagnostic Trouble Codes and Communication issues between modules.

https://www.google.com/search?q=2008+Chevy+Malibu+LS+cranks+but+won%27t+start

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The temperature gauge sensor as you call is for more then just the temperature gauge . The temp. sensor is an input to the PCM -engine computer ! If it were bad you would have drivability problems , the transmission would not shift correctly an the check engine light would more then likely be lit .
Engine Coolant Temperature Gage
The IPC displays the engine coolant temperature as determined by the PCM. The body control module (BCM) receives a class 2 message from the PCM indicating the engine coolant temperature. The BCM converts the engine coolant temperature into a percent gage deflection. The IPC receives a message from the BCM via the serial peripheral interface (SPI) indicating the requested gage position. The engine coolant temperature gage defaults to 38?°C (100?°F) or below if:
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The PCM detects a malfunction in the engine coolant temperature sensor circuit.

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The BCM detects a loss of class 2 communications with the PCM.

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The IPC detects a loss of SPI communications with the BCM.

Your gauge is more suspect then the sensor . gm had a problem with stepper motors that control the pointer for the gauge !

There is no relay on the cooling fan circuit.
If the cooling fan is not operating, check fuse #105 (20 AMP), in the underhood junction box, right front of engine compartment.
If fuse is good then test to make sure fan is getting power.
If no power then could be bad cylinder head temperature sensor, hydraulic fan solenoid, a/c cycle switch or the PCM.
If it has power but doesn't come on then fan motor is bad.

The two most common reasons are low coolant or a sticky thermostat.
Low coolant can cause air pockets in the cooling system, and a sticky thermostat could be slow to open and close.

Your best bet have the vehicle check by a repair shop that has a advanced scan too to check for DTC'S - diagnostic trouble codes in all the modules on the vehicle , which is about 10 . Don't listen to someone who tells you to replace parts without trouble shooting the problem , 9 out 10 times they are wrong an you spent money you didn't need too .

You need to find out the fault code that is stored that is causing the check engine light, the whole thing may be related to one failed part like the temperature sensor or the wiring to it.

mine is doing same thing have changed heat sensor the cooling fan runs all the time and check engine light is on i had it read and thay said the computer is not getting coolant temperature

The cam sensor is on the back of the engine, drivers side. On the side of the head, facing the wheel. Just under the rocker arm cover. Only thing on that side. Four bolts to remove it.

you probably have air trapped in the system. Have dealer or radiator shop bleed system.

I assume your cooling fan is working.

what engine v6 or v8?

SECTION 303-03: Engine Cooling 2001 Lincoln LS Workshop Manual
DESCRIPTION AND OPERATION Engine Cooling The cooling system components include the:

• block heater (optional)
• cylinder head temperature sensor
• fan blade, fan motor and fan shroud assembly
• radiator
• pressure relief cap
• degas bottle
• radiator draincock
• water pump
• oil cooler (optional)
• water thermostat

The water thermostat:

• controls the engine coolant temperature.
• allows quicker engine warm-up.

The degas bottle:

• provides a location for system fill.
• contains coolant expansion and system pressurization.
• provides air separation during operation.
• replenishes the engine coolant to the system.

The fan blade draws air through the radiator to help cool the engine coolant.
The fan motor:

• operates only when the engine is running.
• will not operate when the engine is off.

The engine coolant flows:

• from the lower radiator hose to the water pump.
• from the water pump to the engine block and the cylinder heads.

A closed water thermostat returns the engine coolant to the water pump. An open water thermostat allows the engine coolant to flow to the radiator.
Unsatisfactory coolant materials:

• Alcohol-type antifreeze does not provide adequate water pump lubrication.
  • has lower boiling point
  • reduced antifreeze protection
• Alkaline brine solutions will cause serious engine cooling system damage.

The cylinder head temperature sensor provides a signal to the temperature gauge.

• will invoke failsafe cooling.

The optional block heater:

• electrical heating element is installed in the block cooling jacket.
  • uses a standard 110V (220V in Europe) electrical supply
• keeps the engine coolant warm during cold weather.

The auxiliary water pump (3.9L only):

• provides heater coolant flow boost.
• has a secondary function of providing engine-off cooling.

replace thermostat, this fixed my car, cooling fans keep coolant below temp guage parameters.