The OP (and most everyone else) didn't mention whether the cooler they are adding is an auxiliary cooler or the only cooler they are running. The liquid/liquid cooler in typical factory radiators is a pretty efficient cooler, and if you swapped radiators and are not running the transmission fluid through the radiator you are going to need some pretty good coolers to replace that. Derale claims their plate style coolers with a fan (like the Atomic or Hypercool) will be sufficient as a stand-alone cooler, but I suspect it might be marginal, especially with high-stall converters.
I know it's not a V8, but I was running a 4.0 TJ with a 32RH (3 spd, no OD) transmission swapped in. I was running the original manual trans computer, so the converter was not locking up. I had the fluid running through the factory radiator, then through a Derale Atomic cooler that was mounted under the hood on the passenger inner fender with a series of 1" holes cut in the inner fender to allow airflow in, and hood vents to allow airflow out. Not the best place, but space is kind of limited and was trying to keep it out of the passenger compartment. The fluid temps in the pan would stay 180F or less all day long if I was crawling/riding trails, but at highway speeds for more than 15 minutes the temps would start to climb into the 200+. Since I didn't drive a lot of highway, I just ran with it.
Currently re-doing the front suspension to stretch it, and I have swapped to a shorter Griffin 3" thick, single core radiator with no provisions for transmission cooling. After talking with Derale, I am running one of their Series 10000 16 row stacked plate coolers (32,000 btu) in front of the radiator, and then into the Derale Atomic cooler after that, still under the hood, but with better (hopefully) air flow. Everything is plumbed with -8 hose. Since it isn't running yet, I can't say if it will work, but the theory is that the cooler in front of the radiator will take most of the heat load, and get better at speed, and then the Atomic cooler with a 180F thermostatic switch for the fan) will handle any excess heat load. I also have an automatic computer to swap in if that doesn't seem sufficient.