EXCELLENT POINT and a very big concern in my situation. The guys with manual transmissions only have to deal with engine warm up but with automatic transmissions it's a very different situation.
In my case, I have an automatic transmission (C-6) with an over-sized plate and fin auxiliary transmission fluid cooler as I plan to be in some very hot climate zones in the future but I am in a cool climate zone now. Just from the fan pulling cold air across that aux. transmission cooler ESPECIALLY DURING COLD WEATHER, the extra larger cooler will slow the warming up of the transmission to normal and safe operating temperatures, not to mention the coolant in the radiator staying cold and further cooling the transm. fluid that goes through the internal heat exchanger in the bottom tank of the radiator.... UNTIL THE THERMOSTAT OPENS UP.
SO, I need the coolant mix in the block to heat up fast so the thermostat will open as soon as possible to allow hot coolant into the radiator where it can flow down to the internal heat exchanger in the lower tank and reduce the amount of heat removed from the transmission fluid = so the transmission will warm up quicker. With the check ball in place and functioning, the thermostat should open a lot faster with the engine warm up being faster and be ready to drive, saving warm up time and fuel consumption. At that point I can start out easy and the transmission will come up to temperature quickly. If the thermostat doesn't open quickly I'm concerned about even the slightest damage to my transmission. I want it to last a very long time, the same with all of the work and parts I put into my truck. I will have to depend upon this truck with no breakdowns over some long hauls over mountain ranges and in some remote areas pulling a trailer with valuable belongings in the truck and trailer and I don't want to have ANY kind of breakdown. Or, I might have to leave the truck and trailer unattended to go into a town to try to get the parts I need. Plus I don't want to be on the side of the road having to do any work to it.
I think this transmission warm up is MORE important for the E4OD so DON'T delete that heater hose that goes from a Tee (T) in a heater core hose and the other end goes to the fitting on the lower passenger side tank of your radiator. Surprisingly, a LOT of hot coolant flows through that little hole and it WILL help to warm up your E4OD in all kinds climate conditions. THAT is why the engineers put it there so don't delete it! Unless of course you have a manual transmission with a radiator for an E4OD, then simply plug it with a short piece of heater hose, a 5/8 bolt for a plug, with a long enough smooth shank after cutting the threaded section off and a hose clamp the hose over it.
I have a later style replacement copper radiator in my truck that came from a truck with an E4OD so that's how I know about that fitting and how much hot coolant can flow through it. I also have very good technical perception and understanding of liquid flowing through pipes, pressures, negative pressures, cavitation and heat exchangers and I agree with and trust the engineers who put that fitting there more than I will trust back yard mechanics who have argued that it is of no use and can be deleted!
The right solution for my situation is to have a thermostat to cut off the flow of transmission fluid to that auxiliary cooler, to bypass it until fluid temperature conditions are up enough to open it. I didn't think of that when I installed the larger transmission cooler and I really can't afford to do it now, too many priority things on my truck to fix that cost significant amounts of money and I have a very low Soc. Sec. income. So when cold weather comes again I will either have to install a manual valve or block off the plates and fins so cold air doesn't flow directly through them. The manual valve would be the simpler and better temporary solution.
There is one more important thing that I will put into a reply to genscripter
