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Yes, the temp. does matter. Using cold water will cause the pores in the eggshell to dilate meaning any dirt on the surface can be pulled into the interior of the egg - the part you are eating.
I don't sell eggs to my customers that are more than a month old, although I never have eggs around that long.
For my own family's consumption I wouldn't have a problem with eating an egg that's a month and a half old, so long as I haven't washed off the bloom.
It's possible to buy eggs in the grocery store that are at least 6 weeks old.
ETA: The contracting/dilating thing may be reversed, I'm very tired, but the concept is the same. Use water hotter than the egg itself.