The engine idle fluctuates the temp gauge always reads hot even on a cold start radiator is always hot

An accurate temperature gauge will always fluctuate because the temperature in the engine fluctuates.

Usually the only time this is really noticeable is when the engine has been working hard and suddenly has to wait at a junction or similar and the gauge can rise considerably.

You didn't mention by how much the gauge fluctuates?
As long as it remains approximately in the normal zone it is acceptable but if it climbs into the hot zone or falls into the cold zone it is not acceptable and the cause should be investigated as soon as possible.

Temp gauge fluctuates? From around 200 degrees and up, then back down? This is an air pocket. First check the reservoir for leaks, then check the hose from the reservoir to the radiator for leaks and if it is kinked. No kinks in this hose is important. When I purge these systems, I drive it till hot, then turn sharp circles both ways. In a parking lot. This seems to help purge the heater core. Then refill as necessary. I do this with any car that has the 3.4 or 3.1 engine.

A thermostat should only allow flow after reaching its desired temp, 195, however, if this is just idling and you have a brand new aluminum 4 core radiator then it may really not be reaching temp and reading low because of no load and a great radiator. I assume top of the intake manifold is where your temp sender is? Did you use a laser infra red temp reader and point it at the block in several spots? You may see175, 185, etc all over the side of the eng. The neck of the thermostat housing should be the closest to 195 but the lower hose might read 140 / 150. Alum radiators work awesome so when that thermostat does open it's a rush of cooler coolant. What is it doing when you drive steadily @ 40 - 50 mph? If the gauge reads say 140 and just fluctuates slightly from that then I would say yes, replace the thermostat. If your gauge shows it now reaching temperature then it's just that your radiator is doing a helluva job when it idles. BTW, electric fans? On a switch or temp sender? Or mechanical fan always pulling air even at idle?
Hope this helps

Watch the temp gauge when the electric radiator fans come on. The temp sensor that controls when the fan comes on may be faulty.

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

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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
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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.

The temperature you see on the dash board gauge is not necessarily the actual temperature of the coolant. The engine has a 'coolant sensor' which sends information to the electronic control unit (ECU /PCM) and there is a separate 'sender' which governs the gauge reading you see on the dash board. The sender usually has just one wire connected to the top of it. The sender is basically a heat dependent resistor and the temperature gauge simply reads this resistance. Sometimes corrosion in the electrical connector can inhibit the correct readings, so first disconnect the sender and inspect/clean the pin with a little wire wool. Now check the coolant. First put the interior heater on maximum heat. Run the engine up to working temperature and then squeeze all rubber hoses to help shift any trapped air. Top up the coolant if the level drops when air pockets have been shifted. The following sequence should occur when the engine is warming up. 1) When cold the engine has higher then normal revs. This is due to the coolant sensor (not sender) telling the ECU that the engine is cold and that the injectors should add more fuel to compensate for the cold condition of the engine. 2) Within about a minute the idle revs begin to drop as the coolant sensor detects the engine warming up 3) After about 5 minutes the thermostat should open. You can detect yourself this by feeling the top rubber radiator hose getting hot. 4) If you have an electric cooling fan on the radiator this should switch on about now. If you have a fan driven by a viscous clutch this will engage a little later. 5) after about 2 more minutes the face of the radiator should be becoming hot and the bottom rubber radiator return hose should become warm, then hot.
If you have an electric fan and it fails to come on then check the electric relay and fuse for it. Viscous clutch fans should always show some resistance when turned over by hand when the engine is off, if it spins freely then the clutch coupling is faulty and it will need to be replaced. A sign of faulty fan related over-heating is a car than runs at normal temperature when cruising on the freeway but overheats when standing at the lights; fan engagement is to compensate for the lack of air flow across the radiator core when the vehicle is stationary.
I hope the above helps

Sounds Like A Problem With your thermostat. Good Luck

Definitely check your fluid level in your radiator. Top it off all the way. I've seen that happen multiple times on cars that were low on anti-freeze. If that doesn't work try replacing your thermostat. It's cheap and the easiest place to start if topping off the fluid doesn't get you fixed up.

Here's the thing. The ECU will shut down AC if the engine temperature is too hot. If the coolant temperature sensor is malfunctioning (lying to the ECU) telling it that the temperature is hotter than it actually is, the computer will turn the AC OFF.

you have air trapped in the cooling system. A good indication is that one or both of your heater hoses going into the heater core are cold when they should be hot.
Park facing uphill, raise front of vehicle so radiator cap is higher than top of engine. (You want bubble to get to radiator and out the cap.)
Leave cap on but loose, so bubble can purge.
Turn heater on.
Fill radiator and reservoir with 50/50 mix of antifreeze.
Start engine and run at about 1500 roms until the engine warms up and thermostat opens.
You will know themostat opens when top radiator hose is hot indicating coolant is flowing.
Shut off engine.
Fill radiator and reservoir. Install cap.

please Rate as fixya if this works. good luck