Trans cooler reccomendation...

Yes 4R75W was installed starting in 2004. No expert here, but not heard of them running hotter than other AT's. A trans. cooler is a good addition but not usually necessary unless towing, a lead foot or hot climate and lots of A/C use/heavy traffic. Any of the Mustang Parts retailers have them for sale and of course YouTube is a good go to for installation/recommendations. Definitely a daughter to be proud of!

Transmission coolers will lead to additional problems over time if they make the transmission run too cool. There's a band of operating temperatures and usually air to liquid coolers are way too much unless the system was designed that way. In general you want to avoid adding parts unless you can either show a need (temperature calculations that would show cooling load needed as well as sizing the cooler) or the manufacturer recommends it based on statistical data that they've seen. Short answer is you might over-cool it and have too much clearance between parts (bearings and shafts as well as clutches, bands, etc.) which can lead to slippage, vibration, and other problems.

I've been considering this as well. My daily commute is basically 12 miles each way stop and go. When it is hot out and traffic is heavy, I often see nearly 200* for trans temp on my x4. Seems a little high to me but haven't really found a definitive answer.

200 degrees isn't necessarily a bad thing. The only time you would want to consider additional hardware in this application would be if normal operation is being interfered with. If you were seeing issues with shifting (noise, vibration etc.) you might consider it, but if not you will actually bring the transmission out of the operating range and essentially do worse than without.