I agree with Brian that unless the water pump is leaking it is not likely the cause of the overheating. Based on my experience with the Diesels and older cars I have owned, I will recommend this:

Make sure there are no pressure leaks. Pressure is required for proper cooling. You will know this by leakage or steam.

Replace the thermostat and flush the system. The thermostat is cheap enough, but again not likely to cause your overheating because the style used on these cars tends to break OPEN causing the car to run too cool in the winter...

Most likely you will need a new radiator or at least get yours cleaned out. Yes, you have relatively low miles on the car, but it is age that is a worse enemy to the radiator than miles. These days a replacement is not too expensive nor difficult to install.

I have experienced on two occasions that an otherwise good water pump with some age on it will start leaking after flushing the system and replacing the coolant. If you want to be set for many months to come you might consider just doing it all. Radiator, water pump, thermostat and ALL hoses.

So far I replaced the radiators on every car in my list below except for the 2002 and it fixed my overheating each time.

__________________
02 S500
92 500SL
92 400E (Sold)
87 300E (Sold)
83 300D Turbo (Sold)
75 300D (Sold)
74 240D (Sold after 20 years)