I haven't had much luck with the ready made egg tempera paints, though I have made my own egg tempera paint before using distilled water, egg whites, linseed oil and powdered pigment. Some artists will vary and only use the egg yolk, or the entire egg.
It is an old recipe and it can be tricky. It must be built up in thin layers, but is VERY forgiving. If you allow it to dry, which only takes minutes (similar to acrylic paint), you can continue to make corrections in your painting for as long as you like.
Masters used it way back when because pigments were so expensive to attain, and this way they figured out all their mistakes prior to adding color to their canvases.
Egg tempera if created by hand, creates a luminosity that is more beautiful than anything I've seen before using just oil paint. It takes practice. It is prone to cracking. But...it sure is fun to play with.
Here's a website to the Egg Tempera Society: http://www.eggtempera.com/technical-info/egg-tempe...