Answer:
Birds that live in cool climates lay darker eggs, as darker colors absorb more heat from the sunlight
Birds that live in hotter climates lay lighter eggs to prevent the egg from overheating.
The pigmentation acts to thermo-regulate the internal temperature of the egg, acting as a buffer between the embryo and the outside world. It does this by preventing overheating of the egg, through reflecting the sunlight off the pigmentation, rather than allowing it to be absorbed through the shell