I've overheated my L27 3 times. Once at 90k miles when the water pump went for the first time, and the temperatures just barely hit the red mark. The second time at 180k miles when one of the fans stopped working on a very hot summer day, where the temperature was 2 gauge marks below the red line, and again at 206k where it once again stayed two gauge marks below the red line when my thermostat got stuck closed. None of those caused any damage except for the last time, when it warped my upper intake manifold a bit around the throttle body coolant passages, which ruined the gasket and caused a small coolant leak when the engine was cold. I fixed that using some sealant and a new gasket, and all'* been well for the last 7k miles. That'* just for comparison purposes as to overheating damage.
2005 Pontiac Bonneville GXP - For Sale ----- 1995 Buick Regal GS(X) - L67 madness
2000 Buick Regal GSE - Stock...for now
----- 1987 Jaguar XJ-* V12 - 12>8