PAY ATTENTION to the way the "automatic" transmission operates.
If it can hold the torque converter clutch "ON", you're probably OK in overdrive.
If the torque converter clutch disengages, better to be in 3rd or even 2nd gear with the converter engaged, than a higher gear with the converter unlocked.
Maybe. Verify your trans temp BEFORE adding another cooler.
Consider plumbing the hot trans fluid through the aftermarket cooler, THEN through the radiator cooler. When it's hot, you have two coolers assuring that the trans temp is not overly-warm. When it's cold, you have the engine heat via the radiator to warm the fluid before it returns to the transmission. Speeds warm-up in the winter, prevents overheating in the summer.