Just for a Bleeder Valve Screw!!!

I had my car in for service for two days at the dealer, i got CPO warranty and i had some problems with the power steering fuel pump and the thermostat needed to be changed and other normal routine maintenance. I took it back and while driving to NJ on the night before the snow storm, i ran into an overheating problem that turns into a real nightmare. I had to have my car towed off the NJ turnpike to a safe zone, and then i had to wait until tomorrow morning until the streets were all cleaned up. All this for what? a damn Bleeder Valve Screw that was damaged by the technicians at the BMW service center. I took my car back there today, i took the piece of the screw out of my pocket and placed it on the desk, the service adviser felt so stupid he wouldn't even look at me in the face. All he could say was sorry.

I have a question. My car started overheating like crazy and i was just getting off the highway, into the service area. I didn't leave it on, i turned it off right away so the engine gaskets or the thermostat or other things wouldn't get damaged. How long would it take for the engine to get badly damaged of overheating?