[97tdi]

my car is running hot
i have replaced the thermostat, radiator cap and water pump once already
i am using green anti freeze dealership said it was ok because it was an older tdi
how can i test to see if the water pump is bad other than noticing a leak.
car runs smooth throughout acceleration and idles fine. the car does not miss and i dont see any steam coming out of the tailpipe
so i dont think the head gasket is leaking or cracked.
the coolant fans are working normally as they should. radiator is not leaking and isnt clogged