Do all A bodies have overheating problems?

You didn't mention whether or not a shroud.
I"ve added a factory shroud. I've also tried a Mopar Performance factory style clutch fan and fan. Didn't seem to help.
When i purchased the car, it had a very sick 273 2bbl. Car would overheat anytime I idled in traffic when it was hot out. No factory shroud, 4 blade fixed fan. I just tried to not get stuck idling .
Then switched to a friends 318 4 bbl engine, when we upgraded his car to a 340. Never ran more the 195 in his car. Started having problems as soon as I installed it in my car.
Took the radiator to a radiator shop, they said it was 40% . clogged so they repaired it. No difference. That"s when I upgraded to a 3 core factory style radiator., along with a lot of other changes.
Now with a fresh 340, the problems persist. Today was the first time in hot traffic. I was OK with 190 or so in traffic, but the longer I putted around in traffic, the more the temp climbed.
I'm reluctant to try electric fans again for a variety of reasons. Maybe I need to look at a different type of fan blade.....Larry