Cooling fans in op until engine is shut down . At idle, in traffic, temp gets high, hen wmoving, temp goes back to normal. When I shut down the engine the fans start to run as they are supposed to when the engine is hot. I suspect they do run when the AC is engaged because the temp stays within normal range in traffic or moving.

No switch - the radiator cooling fans are controlled by the PCM which receives a signal from the coolant temperature sensor located at the passenger side end of the engine at the lower right.

What makes you thing it's a sensor ? A lot of thing's could cause this , taking the vehicle to a qualified repair shop is what should be done. They will do a full system scan .
ENGINE HOT A/C OFF
Cooling System Description and Operation

Coolant Warning Messages
The radio will display the following messages if the following conditions exist in the cooling system.
• Engine hot--A/C OFF will be displayed if coolant temperature is above 117°C (243°F). For imports 115°C (239°F).
• Engine coolant hot--Idle engine will be displayed if coolant temperature is above 118°C (245°F).
• Engine overheated--Stop engine will be displayed if coolant temperature is above 123°C (253°F).

Cooling Fan Control - Two Fan System
The engine cooling fan system consists of 2 puller type electrical cooling fans and 3 fan relays. The relays are arranged in a series parallel (S/P) configuration that allows the engine control module (ECM) to operate both fans together at low or high speeds. The cooling fans and fan relays receive battery positive voltage from the underhood fuse block. The ground path is provided at G104.
During low speed operation, the ECM supplies the ground path for the low speed fan relay through the low speed cooling fan relay control circuit. This energizes the low speed fan relay coil, closes the relay contacts, and supplies battery positive voltage from the low fan fuse through the cooling fan motor supply voltage circuit to the left cooling fan. The ground path for the left cooling fan is through the cooling fan S/P relay and the right cooling fan. The result is a series circuit with both fans running at low speed.
During high speed operation the ECM supplies the ground path for the low speed fan relay through the low speed cooling fan relay control circuit. After a 3 second delay, the ECM supplies a ground path for the high speed fan relay and the cooling fan S/P relay through the high speed cooling fan relay control circuit. This energizes the cooling fan S/P relay coil, closes the relay contacts, and provides a ground path for the left cooling fan. At the same time, the high speed fan relay coil is energized closing the relay contacts, and provides battery positive voltage from the high fan fuse on the cooling fan motor supply voltage circuit, to the right cooling fan. During high speed fan operation, both engine cooling fans have their own ground path. The result is a parallel circuit with both fans running at high speed.
The ECM commands the low speed cooling fans ON under the following conditions:
• Engine coolant temperature exceeds approximately 94.5°C (202°F).
• A/C refrigerant pressure exceeds 1447 kPa (210 psi).
• After the vehicle is shut OFF, if the engine coolant temperature at key-off is greater than 101°C (214°F), the low speed fans will run for a minimum of 60 seconds. After 60 seconds, if the coolant temperature drops below 101°C (214°F), the fans will shut OFF. The fans will automatically shut OFF after 3 minutes, regardless of coolant temperature.
The ECM commands the high speed fans ON under the following conditions:
• Engine coolant temperature exceeds approximately 104.25°C (220°F).
• A/C refrigerant pressure exceeds approximately 1824 kPa (265 psi).
• When certain DTCs set
At idle and very low vehicle speeds the cooling fans are only allowed to increase in speed, if required. This ensures idle stability by preventing the fans from cycling between high and low speed.

DTC P1258: Engine Coolant Overtemperature - Protection Mode Active

Your vehicle cooling fan's are controlled by three relay's , couple of fuse's an the PCM - engine computer . The engine coolant temp. sensor is a input to the PCM , when engine temp get's to 212 the PCM will turn on the cooling fans in low speed . Checking to see what the actual temp is with a scan tool an a infrared thermometer at the thermostat housing ,an looking up the specification's in a service repair manual is how to diagnose . Not guessing an replacing parts . Plus learning how the cooling fan's work .
Relay Driven Dual Cooling Fan Diagnostics Reading factory service info as to how they work also would be a good idea .

Cooling Fan Control - Two Fan System
The engine cooling fan system consists of 2 puller type electrical cooling fans and 3 fan relays. The relays are arranged in a series parallel (S/P) configuration that allows the engine control module (ECM) to operate both fans together at low or high speeds. The cooling fans and fan relays receive battery positive voltage from the underhood fuse block. The ground path is provided at G104.
During low speed operation, the ECM supplies the ground path for the low speed fan relay through the low speed cooling fan relay control circuit. This energizes the low speed fan relay coil, closes the relay contacts, and supplies battery positive voltage from the low fan fuse through the cooling fan motor supply voltage circuit to the left cooling fan. The ground path for the left cooling fan is through the cooling fan S/P relay and the right cooling fan. The result is a series circuit with both fans running at low speed.
During high speed operation the ECM supplies the ground path for the low speed fan relay through the low speed cooling fan relay control circuit. After a 3 second delay, the ECM supplies a ground path for the high speed fan relay and the cooling fan S/P relay through the high speed cooling fan relay control circuit. This energizes the cooling fan S/P relay coil, closes the relay contacts, and provides a ground path for the left cooling fan. At the same time, the high speed fan relay coil is energized closing the relay contacts, and provides battery positive voltage from the high fan fuse on the cooling fan motor supply voltage circuit, to the right cooling fan. During high speed fan operation, both engine cooling fans have their own ground path. The result is a parallel circuit with both fans running at high speed.
The ECM commands the low speed cooling fans ON under the following conditions:
• Engine coolant temperature exceeds approximately 94.5°C (202°F).
• A/C refrigerant pressure exceeds 1447 kPa (210 psi).
• After the vehicle is shut OFF, if the engine coolant temperature at key-off is greater than 101°C (214°F), the low speed fans will run for a minimum of 60 seconds. After 60 seconds, if the coolant temperature drops below 101°C (214°F), the fans will shut OFF. The fans will automatically shut OFF after 3 minutes, regardless of coolant temperature.
The ECM commands the high speed fans ON under the following conditions:
• Engine coolant temperature exceeds approximately 104.25°C (220°F).
• A/C refrigerant pressure exceeds approximately 1824 kPa (265 psi).
• When certain DTCs set
At idle and very low vehicle speeds the cooling fans are only allowed to increase in speed, if required. This ensures idle stability by preventing the fans from cycling between high and low speed.

Cooling fan relay's High speed relay K-46 Engine cooling fan relay K-45 .Located in the under hood fuse box. The PCM - engine computer energizes the relay's when the input from coolant sensor shows it's over temp . Check out videos on youtube . Cooling Fan Repair On Your Car Check out a few other videos

{: ) The engine control module is programmed to protect the engine by disabling the starting system whenever it detects that the engine temperature is beyond safe limits. Depending on how fast the engine cools, it will resume normal starting after cooling down for a while.
A diagnostic scan tool readout can give you a quick idea about the possible causes of your engine overheating. For the meantime, as soon as you can start the vehicle after cooling down, drive the vehicle and try to turn off or minimize the loads , and avoid traffic sitting as possible, just enough time to reach home or a nearby service shop.
There are several things that need to be checked:
The coolant level and quality, and check for signs of coolant leaks.
The cooling fans,are they operating as designed? Check for fan blades damage or cracks.
The water pump could be faulty. Check also the engine belt.
The engine oil.
If the engine temperature sensor is faulty, it can also bring inaccurate signals and may affect operation of the cooling fans.
Check fuses and relays that power the cooling fans.

You probably need to bleed the cooling system properly.

Open the cooling system bleeder screws.

Slowly fill the cooling system with a 50/50 coolant mixture until coolant runs freely out of bleeder screws.
Close the cooling system bleeder screws
Install the coolant pressure cap
Start the engine.
Run the engine at 2,000 - 2,500 RPM until the engine reaches normal operating temperature. (midway on gauge)
Allow the engine to idle for 3 minutes.
Shut the engine off.
Allow the engine to completely cool.
Top off the coolant as necessary.
Run engine again at 2000 - 2500 RPM until the engine reaches normal operating temperature.
Allow engine to idle until cooling fans come on. It should come on with the gauge about 3/4 of the way to red. - if it gets to where is touches the red, shut down immediately.
When the fan comes on, put your hand behind the fan and observe the temperature of the air coming from the fan. It should feel hot. If it is blowing cold air, the coolant is not circulating through the radiator like it should. This could be caused by lots of things including an improper/defective thermostat, corroded water pump impeller, or a blown head gasket.

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.

Cooling fans only run when the temp,of the coolant get to about 215 to 218 degrees,and shut them selves off,when the engine cools down,if they do not cut off,the engine is not cooling down,now,if the ac is on,the cooling fans will stay on until the ac is shut off.

I am not an expert on Mazda vehicles but sounds like your fan temperature sensor is not working properly. My fan comes on low speed when the temp hits 205 and goes to high speed at 220 or when the air conditioning is on. You had better get it checked by your dealer or service tech.

Check the auxiliary cooling fan for operation. As the engine temp rises, it should kick on to bring the temp down. U may have a bad motor on the fan, or more likely a bad fan switch.