My approach to an issue like this is: First - if you haven't already - find out what your coolant temp actually is. If you already have a good quality aftermarket temp gauge (preferably mechanical) installed, then you can move on to other considerations. If you still have the original temp gauge, though, I wouldn't necessarily trust it. (I'm surprised how many people do.) If you don't want to put a new gauge in, then an infrared temp gun is in order.
Flushing out is a good idea, as others have said. If you have excessive rust, folks at the AACA forum have suggested Evaporust, which I've tried and has worked well. You keep it in the system for a while, so of course winter isn't a good time to use it since there's no antifreeze protection.
Beyond that, I put a radiator from Wizard Cooling in my '61 Merc 352, and I was very pleased with the quality of their stuff, but they aren't original looking or cheap. It was aluminum, so it's probably advisable to use a zinc sacrificial anode in the system. The Wizard radiator is still working good and keeping the engine cool enough...but the original radiator should be good enough to keep it cool, if it's working. Shrouds are supposed to help, though I made one from a couple of half shrouds from Speedway and I can't say how much they help.
Worn out engines can cause overheating, too. Of course, all the old cars I've owned have run hotter in stop and go than on the highway - kind of the nature of the beast - so knowing what your temp actually is would be important. Good luck
