1968 Barracuda. Is this the stock radiator?

It should still provide decent cooling if it is not clogged up. Are you going off of the stock gauge or ? to determine how hot it is running. Checking the basics is a good start. Is it timed correctly and carb tuned correctly ? is there a good working thermostat in it? I will agree having a shroud will help it keep cool but i had run mine for several years without one and never ran hot.
I am going off of the stock gauge. How accurate that gauge is is a good question. It gets all the way up to the final bar before the "H", and that's on the interstate on a 40 degree day. I do not know if the carb is tuned correctly, or if the thermostat is working properly. I just had the radiator flushed so it probably needs topped off too. These are things on my TTD list.