Maybe depending on the amount of oil in the radiator.

Your radiator has a tank for the trans fluid to flow thru. This is to help warm the trans when cold and cool the trans fluid when it gets to operating temp. Sometimes there is a leak in the tank that causes contamination.

I would fix this first and see what your cooling situation is like afterwards

Allen Here's a novel idea, let's not throw a bunch of parts at the car hoping it will fix the problem and instead spend a little time diagnosing it first. Life was a little easier when I was just a wrench.