My Ride is HOT!! and not in a good way!

Alright fellas can somebody please help me out. My 65' is burning up!! I recently dropped a rebuilt 350 in her and am still running the stock radiator. Mind you the radiator is about a year 1/2 old so its in great condition. But I cant take the nova out for 30 mins w/out it overheating! i stop at a light or get stuck behind a few slowpokes and the needle starts climbing from 180-190 to 190- 215/220 reeeeally fast!! so what im asking is after i get this radiator flushed and properly cleaned and the block flushed out would that radiator keep the car cool, especially at cruising speeds or during city driving?? A hot cars no fun when it becomes literal!