250 is high and can be cooled off with a good cooler. I generally run about 80* over ambient temp normal driving. On an 90* day I see temps of about 170*.
Pulling hard 12k 5th wheel camper I see temps of 100* to 110*over ambient temps. On a 90* day I have seen temps set around 200* pulling.
The stock setup runs through the radiator then through the tranny cooler(which if stock is junk). The temps will be cooled down to no less than the radiator temps, example if your transmission fluid temps are 200* running into the radiator and the radiator temps are setting at 180* that is the least temp it will see before going to the cooler, additional cooling is accomplished through the tranny cooler. Which with the stock cooler is not much.
If it were me I would remove the stock cooler get a good stack plate cooler, flush the lines and take a new reading. If temps do not improve your problem may be deeper.
Hope this helps