That is a good temperature. Just make sure that it reaches at least 165F on a winter day, that will allow all the moisture to boil off from the fluid. You might need to cover the cooler in front of the radiator during snowy conditions.
You might see 205 - 225 during a climb in the mountains, and this is normal. However if towing, and you start to see 210 on flat lands, and 235 in the mountains, then you should install a larger cooler.
There is a chart for how long transmission fluids will last. At 300F, you should not drive more than about 100 miles before replacing the transmission fluid. At 250, the fluid will last 5,000 - 8,000 miles. At 235, it will last 12,000 miles.
At the temperature below 200, it should last the full normal change interval, such as 15,000 to 25,000 miles, depending on your manufactures recommendations for "Normal" use.
Fred.