whats likely is if the transmission is an automatic then it will be cooled with engine coolant and its possible that where the transmission pipes enter the radiator they are cracked and then allowing coolant and ATF to mix
so check the coolant header tank for signs of oil mixing and if its present then I'd consider replacing the radiator
do you still need help?
Bear in mind that the site takes a deposit from you at the beginning andthis is held by the site until you rate my answer at which point the cash issplit between the site and the expert. I am only paid for my work on thisquestion if you rate my answer, using the star system at the top of the screen. Please do not forget! Thank you