I'm not aware that there is an A/C shutdown function at high engine temperature.

At idle and stop and go driving in hot weather, expect the temperature to go up to as high as 105C. A this point the dual electric fans will engage at high speed and they will rapidly bring the temperature down to about 100C where they disengage. This cycle will continue until you get up to steady speed such as freeway cruising where the temperature should run about 90 in hot weather.

Even though the mechanically driven fan' thermo-viscous clutch tightens at bout 100C this fan does not provide much air flow at idle speed, but the electrics at high speed are like a hurricane, and if the temperature doesn't drop rapidly, the radiator is probably clogged and needs to be replaced. Same situation on the highway. If it runs consistently over 90 at freeway cruise the radiator is probably clogged with deposits, which signficantly reduces its heat tranfer rate.

You can test the fan operation by letting the car idle in hot weather. At about 100 rev the engine to about 2000. You should hear "fan roar" and feel greatly increased flow realtive to flow at below 100. Let the engine continue to idle and check for engagement of the dual electric fans at about 105C. Do this test first with the A/C off. The do it with the A/C on and Min on the temperature dial and the windows open. The electrics should engage periodically at low speed based on the A/C pressure swtch. This will help cool the engine, but the coolant temp will probably evenatually creep up to 105, where the electrics should engage at high speed. If the A/C shuts down, check the freon level. It may be low.

The gage has a hash mark at 100 and 120 is the top. So what it the highest reading you are seeing - relative position of the needle to the above two hash marks?

Duke