According to the United States Library of Congress, it's possible, but not probable, that you could fry an egg on a sidewalk during a hot day. Eggs need to reach a temperature of 158 °F (70 °C) to cook through. Sidewalks can usually get up to 145°F (62.778°C). The hotter the day, the more likely your egg will fry.

Using a good heat conductor (i.e. a frying pan) is also important. A concrete sidewalk isn't the best conductor of heat. Neither is blacktop pavement, but it will get warmer than the sidewalk. Even hotter still is the hood of a car, which is more akin to a frying pan than pavement or concrete. (Though attempting to cook an egg on your car may ruin your paint job.)

The question is so intriguing that the city of Oatman, Arizona, even holds a Solar Egg Frying Contest every year in a nod to the platitude and the heat.

More Info: www.loc.gov