I'm in the Phoenix area (Desert Hills / New River) and my '65 / 352 was my best friends daily driver for about 5 years when we were kids. Pretty sure it has a <insert your local "cheap" parts store here> sourced radiator and neither he or I ever had cooling problems with the car. This is with a simple arc of sheet metal over the ancient "flexi-fan" acting as a shroud. He drove it daily in city traffic and we spent many 100+ degree nights idling in creeping traffic while cruising Central.
I'm not suggesting that going cheap on a radiator - when I replace this one I'll probably do some sort of overkill aluminum unit - probably from Ron Davis or someone like him - but I'd be pretty surprised if a mild 390 would cause problems for an OEMish radiator if you get decent airflow through it.
Just my 2 cents...