The transmission overheat comes up from the engine getting too hot. I think the PCM calculates transmission temperature as a function of engine temperature, and thus a temp overheat will cause a trans overheat code. So, I'd dismiss the trans overheat warnings/codes at this point, just concentrate on the engine cooling system.
Did you bleed the air out of the cooling system? If you've just filled the cooling system, and didn't bleed the air out, you might have air bubbles that will cause the overheat. If its only been a drive or two since you've done this, then its likely air bubbles, they often work their way out of the system after a couple warm ups, cool downs.
Confirm the trans cooling fan is working, if its not that is guaranteed to cause an overheat in certain circumstances, but normal running in others.
Check the cooling system is holding pressure, the hoses should be hard when its warm, if they are just as soft as when they are cold, its NOT holding pressure. The cooling system holding a higher pressure increases the boiling point of the cooling fluid, if the system can't hold pressure, it will stay at ambient pressure and the fluid is more likely to boil, and once it does boil, boom, you're overheating.