I'm not a certified mechanic. I live in the deep south. It gets hot here a lot. Here are the steps I would do and have done on my 1990 300E.
Replace the Thermastat
Replace the cooling hoses.
Change the Radiator
Change the coolant paying particular attention to whether the coolant called for is green or orange.
When you change the coolant, unscrew the block housing plug and empty that as well.
Change the water pump
Lastly, there is a product on the web that kicks your electric fans on if your temp goes above 101 degrees Centagrade. It costs 44.00 when I put one in my car. You can do a web search for mercedes fan cooling thermastat search. It works great.
Actually, I never replaced the water pump but it's a good idea as you will be staring at it when you change the radiator. Sounds expensive but if you do all the work yourself and STICK to Mercedes original equipment only you will wind up with many years left in your car. These cars don't heal up after they heat up. Good luck. Hope this helps.