You are making a wise decision going with a new radiator (or at least a new core, which costs as much as a new radiator). Why spend thousands of dollars on an engine rebuild and then try to cool it properly with a gummed up, plugged up, brittle old pile of scrap copper?
I too have a Berg's in my 30 Cabriolet. Nothing against Brassworks, they just didn't have a radiator when I needed one. Anyway, I am in South Carolina where it is beyond "hot" in the summer and my radiator temperature is consistently in the upper 150 degrees range (i.e., 155-159). The engine temperature, measured at the head with an IR gun, is around 170 degrees. A friend of mine suggested that this is too cold for the engine to operate at. I know in the winter time, it runs quite cool and a thermostat would make sense.