Which "OEM" fan clutch are you using? Ford discontinued the fan clutch for the automatics long ago, now all you can get is the YB463 Motorcraft fan clutch, which is really only the correct clutch for those with a 5-speed manual. Combine that light-duty clutch with a 195 degree thermostat in 110+ degree heat, and yeah, it'll get hot real quick with the load the A/C puts on the engine.
The 180 degree Stant Superstat (~$5) and the Hayden severe duty fan clutch make for a really good cooling combo in hot hot HOT climates, especially with the 11-blade fan.
If the temps climb past the L in NORMAL at idle even with this combo, there's some other issue either inhibiting coolant flow or putting a strain on the engine. A/C compressor clutch, the A/C system low on lubricant, gunked up coolant passages in the engine from mixing too many different types of coolant, etc.
You may want to do a full cooling system drain, filling with distilled water, and doing the drain/refill/air purge several times until the system is just pure distilled water, THEN draining and refilling with a gallon of good coolant (Zerex G-05 is good stuff), and topping off with distilled water for a 50/50 mix (system is ~2 gal so mixing in a gallon of coolant and the rest distilled water makes it easy). Using tap water with minerals and other contaminants, along with several types of mixed coolant in the sytem, can lead to deposits, buildup, and blockage, making for poor coolant flow and heat transfer.