Either way is an improvement over stock. A larger cooler will be sufficient to be run by itself, and that would likely keep the fluid the coolest, since the radiator is running around 200 degrees when the engine is warmed up.
-91 Cougar LS, coming soon, complete overhaul with a 427" Windsor.
-90 XR7 5-speed black on black w/sunroof, MP2, coated rotors, double intercooler, 15%OD, ported heads, comp stage 1 cam, 85mm TB, 90MM LMAF, 80# injectors, and ported big valve heads
-98 Mark VIII LSC, Procharger P600b, TR3650 swap and 3.73s.
-90 SC Automatic rustbucket winter beater
-97 Tbird Sport 4.6 Nice weather daily driver
-"Your buddy Mike is INSANE!" -ClintD's dad
In cold climates some prefer to run it with the radiator so it warms up quicker, I liked running mine by itself since there's no risk for contamination if there's an internal leak, plus I was able to route the lines cleaner