yes they can be over cooled, ie a big radiator and no thermostat...this increases wear particularly on the cam lobes significantly.
A big radiator wont overcool your engine if your using the right thremostat. For an A series i ran a gemini radiator with a 80 degree C Nissan factory thermo, plus I ran an oil cooler as well. Both indicated temps were 80 degrees C and thats where you want to be. No mater what the exernal temp was or how hard i thrashed in in a race 80 degrees and wouldnt nove.