If you have a temp gauge try it with the old radiator and see. Just watch the temp gauge with the new motor and if it starts getting hot (like 200-215 degrees) shut it down and get a new radiator.
I personally think you would be OK with a 3 core stock radiator and a 383 as long as the radiator is in good shape. A 2 core radiator would be pushing it and you will probably overheat.
E85 racer and E85 carb builder
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68 Camaro, E85 powered 427" small block. 9.96 @ 133 MPH, 1.319 sixty foot on motor. 5.92 eighth @ 116 with a 1.42 sixty breaking beams with back tire on the bottle