What year/model is you unit. Also i might not be correct but is the oil engine or transmission (red or black).
Sorry but I'm old school and it is transmission in the rad. reason engine you want to keep as cold as possible. So separate cooler if you have one. Transmission you want hot (to a point) so with the rad/Waterloo to heat it up before moving.
tranny fluid (red) runs thru the passenger side radiator end tank. the radiator has tons more cooling capacity under all but the most extreme conditions and water to fluid heat transfer is very effective. a small core inside can knock down Temps much better than air in front of the radiator. I personally don't agree you need to warm tranny fluid, it's as thin as water at room temp and compressed to very high pressures, which adds heat. but I base that off nothing besides my experience and I don't live in Alaska or something. running it thru the end tank is for cooling more than warming, I have a feeling tranny temp without a cooler would get hot before the engine on a cold morning at idle anyways. compressing a fluid to high pressure adds tons of heat.
there's a great towing add on cooler thread around here somewhere. guys tested all kinds of configurations. a large front mount alone didn't cool as well and raised coolent Temps by blocking air flow. the best they found was a large add on cooler in the front mounted down low and opening up the fake lower grill, running fluid thru the radiator first and then down to the large add on and then to the tranny.
today's good oil can handle higher temperature for short amount of time without engine damage. I've send well over 300deg oil Temps in track cars without any engine damage, just needs to be changed often. shouldn't be doing 10k mile oil changes with abuse like that. so being that your also can't have two coolers in the same end tank, that leaves the drivers side the only place for the oil cooler from the factory. it is a bit hotter over there, the coolent gauge is located in the cylinder head near the exit. so that should show the max water temp your oil cooler gets run by it, oil sees that or less, which is fine. honestly, these trucks don't have physical oil temp sensors, what's reported to the scanner is just some math the ecm does. if you used this as a tow vehicle (or added boost) and wanted to know actual temp, you'd have to add on a external sensor. I wouldn't worry about it for the average driver. only the guys towing huge rv's in the mountains would I be worry about the oil Temps, especially if you have the factory option that routes it thru the radiator to keep it in check. that and these afm trucks need frequent oil changes anyways.
so yeah red passenger side, black drivers side