does old radiator cause overheating?

[throne7]

1987 260E

My temperature gauge would hit 100Celcius and stays there during city driving. Once I am on the highway, it would drop down to 75 to 80Celsius. Oh and once I pop open the hoods after a bout of city driving, I wouldn't dare touch anything in the engine compartment, it's HOT! Can't even hold the transmission dip stick.

I have been pondering about this slight overheating my car is experiencing and I wonder if it's because the radiator is old.

I guess if the core is all plugged up, it would cause the engine not to be cooled adequately right?

Is there anyway one can check to be sure if the radiator is up for replacement?