I think 4 speed cars got the 24 inch radiator as well. Not sure.
No the 4 speed car did not get the 24 inch automatically. The 24 inch is the heavy duty radiator and it would typically be added if that the car came with A/C. The base 69/70 GT350 4 speed(no A/C) typically got the 20 inch from the factory. With that said If you are pleasure driving the car and it runs
even a little hot I would change to the 24 radiator. I am not sure what the OP has been running now since he didn't say the size(common for radiators on 50 year cars to get switched around)but the 24 inch has a huge amount of cooling capacity over the 20 inch.