To manage the incubation process correctly, we want to create a specific temperature inside the egg. As we don't want to destroy the egg during the process of measuring, we usually measure the temperature of the shell instead of the temperature of the inside of the egg itself.
This measurement gives a good indication for the temperature inside the egg, but is not totally identical, especially not during the warming phase and in the later stages of incubation. Especially later in incubation the embryo is producing heat that will be transported to the surface of the shell, which means there is a gradient in temperature from the inside of the egg to the shell.
As we can imagine, the size of the egg will play a role here as well. A bigger egg will have a larger gradient, simply because there is a bigger distance between the center and the shell. This means that in order to create an identical temperature at the center of the egg, an ostrich egg at the end of incubation will need to have a lower egg shell temperature than a chicken egg, for example. But also within chicken eggs, the size of the egg will have a (minor) influence on the relation between egg shell temperature and center temperature (or embryo temperature).
Gerard van Beek (at that time researcher at the Spelderholt research institute in the Netherlands) has worked out the physical model that describes the relation between egg size, egg shell temperature and embryo temperature. For everybody who is interested in eggs, temperature and physics, and who is not afraid of physical formula's, download the article and enjoy the reading!