My engine overheat when A/C is running on a slow moving traffic or on parking.

the thermostat was not the problem but the viscous fan hub ( fan clutch) is
while it is spinning , there is no drive action when idling ( as at lights , slow traffic , hills in low gear etc) and so it is not pulling air through the radiator when needed
your statement that the temp reduces as soon as you start moving means that with forward movement the air is flowing through the radiator and cooling the coolant

Engine is too hot which is burning oil and road dirt off the engine. Sounds like a bad thermostat or a water pump problem. The radiator may be partially blocked too.

Did you check/replace the thermostat? Another possible cause may be hair line cracks in the head(s).

there are 2 or 3 fans up front on all A/C equipped cars.
the fan closed to engine (rad rear) turns on parked and idling
all engines will overheat parked, if the fan goes dead.
so are you saying this fan is dead.?
if it dont overheat moving fast then the cooling system is usually good
and then you stop at a traffic light this fan must turn on.
on cars with 3 fans , some stage up, 2 on if too hot. or all 3 on.
the FSM covers this logic clearly.
in the USA car.
the element has 2 fans (some engine options my differ)
the right fan is for A/C
and left fan is for engine cooling, (im looking at alldata.com to see that)

the fan turns on via a relay that he PCM controls
the PCM see the ECT sensor in the engine go to over say 225F and
it closes the relay, and the fan spins at full speed.

fuse 4 runs this relay, in the fuse box
the relay and fuse are named
radiator fan.

Could be low on coolant, the cooling fan motor, a relay, or the fuse among other things.
A mechanic would check for power at the fan motor after checking the fuse.
Is the check engine light on ?

If it overheats on the freeway or constantly moving over 35 mph, it will more likley be the radiator blocked upped.

If it overheats only in slow moving traffic, it will likley be a thermo fan issue.

If it overheats all the time and is losing coolant it could be a blown head gasket.

It's the first hint about the new car you really need.

At idling speed an engine does build up a lot of heat and the cooling fan will kick in. In slow moving traffic or traffic jams the temperature gauge can touch the red - particularly on hot days. The reason it cools down when you start moving is because of the air flow through the radiator.

Presumably there are no leaks from the cooling system otherwise you would have mentioned it. In normal circumstances the fan will not be running as you are driving at speed, as the air-flow through the radiator is sufficient to cool things. The fan only kicks in to get rid of excess heat - and this usually occurs at idling speed or after you have parked the car.

If the fan is running all the time as you drive, this points to either a fault in the fan switch, or the car is running too hot. presumably in normal driving the fan isn't running and the temperature gauge reads normal?

It is common - in stationary traffic many cars overheat (particularly big engined models) try to stall and 'cut out'. Restarting can be difficult until the engine cools down.

Is your car overheating in normal driving conditions or just at idle speed? Overheating in normal driving conditions can be caused by things like a failing water pump, blocked radiator, collapsed hose, faulty thermostat or, in the worst case scenario, cylinder head problems.

Overheating at idling speed is 'common'. Check your coolant level. If your car isn't using/losing coolant then there probably is no major problem. You can flush out the cooling system and refill with new coolant - and also check your radiator. Are the cooling fins crumbling with age? Or maybe they're partly clogged with insects and debris from the road? A blast with a hosepipe wil sort that out ..

The question is how much does your car overheat in normal driving? If it doesn't .. it appears as though you have nothing to worry about as such. Most cars have 2 speed fans... the 2nd faster stage kicks in at some point dependant on engine temperature. Perfectly normal.

THE ENGINE IT WONT CRANK IF OVER HEATED CHECK COOLANT LEVEL IF LOW ADD COOLANT.REPLACE THERMOSTAT AND RADIATOR PRESSURE CAP.IF ENGINE STILL OVERHEAT AT A STANDSTILL OR IN A LONG LINE OF SLOW MOVING TRAFFIC.COOLANT FAN SHOULD COME ON.IF ENGINE OVERHEAT CHECK TO SEE IF COOLANT TURNS ON IF NO.CHECK COOLANT FAN FUSE AND RELAY.IFBOTH OKAY HOTWIRE COOLANT FAN TO SEE IF FAN RUNS IF NO REPLACE COOLANT FAN MOTOR. IF FAN RUNS PROBLEM COULD BE PCM OR THE COOLANT TEMPERATURE SENSOR FAULTY OR DAMAGE WIRE CONNECTOR TO COOLANT FAN.USE A CODE SCANNER TO LOOK FOR PCM OR ECT FAULTS.IF EVERY THING CHECK OUT OKAY LOOK AT ENGINE OIL DIP STICK.IF IT LOOKS LIGHT BROWN OR LIKE MILK SHAKE YOUR HEAD GASKET BLOWN.MAKE SURE YOU HAVE 50/50 ANTIFREEZE AND WATER TO ENGINE TO HELP RAISE BOILING POINT.WHEN OUTSIDE TEMPERATURES HOT.

Sounds like your theorem stat might need changed