I have a new tranny, and it gets just as hot as my old tranny. We do have a tranny cooler already. Not sure what good it would do to add another one?
I am with LDUB, if the lights not on, I would not worry. My light has been on twice, while trying to plow up a sand ledge. I checked the fluid at Uwharrie, no problems, still looked great. To clear the light, put it in neutral, bring RPMs to 2500 or so and wait a minute, everything cooled down quite nicely.
I would not worry about the hot tranny, I think its normal.
Kilbys may not be helping, but I doubt it makes that much difference.