I think this site does a good job in talking about storing eggs for incubation, whether you use a broody or an incubator.
Texas A&M Incubation site
http://gallus.tamu.edu/library/extpublications/b6092.pdf
Mother Earth had a nice article and experiment on storing eggs for eating a while back. Under certain conditions they will last weeks if not months on your kitchen counter. But they normally last longer in your refrigerator.
When a chicken lays an egg, she puts a layer called bloom on it that helps prevent bacteria from entering the porous egg shell. If you have ever seen an egg that was just laid, it is wet but it dries off very quickly. That wet stuff is the bloom. If you wash the egg or rub it off, like using sandpaper to remove dirt, you take the bloom off. Then that egg needs to be refrigerated. Bacteria do not multiply very fast in a refrigerator so the egg will still last a long time.
Something else about washing an egg. The egg shell is porous. If the water has bacteria in it, then that water might be absorbed by the egg and any bacteria in the water can be carried inside the egg. I think this part is overblown a bit, but commercial operations wash eggs in water that is about 10 degrees warmer than the egg. The theory is that the air in the air sac will shrink if it cools off and create a suction on the egg, bringing water into the egg through that porous shell if the egg is wet. If you wash it in warm water, the air sac expands and keeps the water from coming inside. Then you dry the egg before you refrigerate it so there is no water to bring bacteria in.
If the bloom is intact and your kitchen temperature is not too hot, the eggs will last weeks on the counter. If the temperature is pretty warm, then the egg is at more risk because that is a better cindition for bacteria to multiply if it ever gets in.
Another consideration. If a fertile egg is kept at incubation temperatures, it will develop. If the kitchen is that hot, I don't want to be working in there anyway. But a fertile egg does not need to be that hot to get some development. I don't know what the critical development temperatures are. It won't hatch, but you could possibly get some development in the low 80', maybe even he upper 70's. If your kitchen temperature is warm, I suggest refrigerating your eating eggs.
So if the bloom is intact and your kitchen is not too warm, they are fine for weeks on the kitchen counter. That is what I normally do. But if the egg is wahed or your kitchen is hot, the refrigerator is best. In Texas in the summer with the AC off, I'd refrigerate.
