Thoughts on plumbing in an aftermarket transmission cooler for my application / driving style & environment?

Gen1 SBC Chevy 350 w/ TH350 tranny in a '78 Jag XJS - 2400 stall speed
Daily driver and live in Texas - never anticipate driving on snow but may drive on nice cold-weather days; I could foresee 'occasionally' driving on days with temps in the mid 30's as the lowest from time-to-time.

Route the lines 'only' thru an aftermarket cooler or better to run in series and include the factory radiator?
Is the radiator recommended for warming up the transmission in my application?
I'm assuming the radiator is not needed but please chime in with thoughts.